%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT139+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:27:19 AM UTC 2026
% Result : Theorem 89.82s 23.48s
% Output : Refutation 92.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 525
% Syntax : Number of formulae : 1097 ( 253 unt; 0 typ; 2 def)
% Number of atoms : 3140 ( 912 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 30642 ( 438 ~; 169 |; 311 &;28179 @)
% ( 107 <=>;1438 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 106 ( 103 usr; 20 con; 0-6 aty)
% Number of variables : 4169 ( 0 ^;4110 !; 57 ?;4169 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_member_decl,type,
c_member: $i > $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_decl,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(c_Product__Type_OPair_decl,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(v_a_____decl,type,
v_a____: $i ).
thf(v_b_____decl,type,
v_b____: $i ).
thf(v_P_____decl,type,
v_P____: $i ).
thf(v_c_____decl,type,
v_c____: $i ).
thf(c_Arrow__Order__Mirabelle_Obelow_decl,type,
c_Arrow__Order__Mirabelle_Obelow: $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Orderings_Oord__class_Oless__eq_decl,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Orderings_Oord__class_Oless_decl,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(tc_Nat_Onat_decl,type,
tc_Nat_Onat: $i ).
thf(class_Lattices_Osemilattice__inf_decl,type,
class_Lattices_Osemilattice__inf: $i > $o ).
thf(c_Lattices_Osemilattice__inf__class_Oinf_decl,type,
c_Lattices_Osemilattice__inf__class_Oinf: $i > $i > $i > $i ).
thf(tc_HOL_Obool_decl,type,
tc_HOL_Obool: $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(c_Nat_Osize__class_Osize_decl,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(c_List_Orotate1_decl,type,
c_List_Orotate1: $i > $i > $i ).
thf(c_List_Olistrelp_decl,type,
c_List_Olistrelp: $i > $i > $i > $i > $o ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i > $i ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(c_List_Osplice_decl,type,
c_List_Osplice: $i > $i > $i > $i ).
thf(c_Relation_Otrans_decl,type,
c_Relation_Otrans: $i > $i > $o ).
thf(c_Transitive__Closure_Ortrancl_decl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(class_Lattices_Olattice_decl,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Relation_ODomain_decl,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Relation_OId__on_decl,type,
c_Relation_OId__on: $i > $i > $i ).
thf(c_List_OdropWhile_decl,type,
c_List_OdropWhile: $i > $i > $i > $i ).
thf(c_List_Olistrel_decl,type,
c_List_Olistrel: $i > $i > $i ).
thf(c_List_Olistrel1_decl,type,
c_List_Olistrel1: $i > $i > $i ).
thf(c_List_Olistsp_decl,type,
c_List_Olistsp: $i > $i > $i ).
thf(c_FuncSet_Oextensional__funcset_decl,type,
c_FuncSet_Oextensional__funcset: $i > $i > $i > $i > $i ).
thf(c_FuncSet_OPi_decl,type,
c_FuncSet_OPi: $i > $i > $i > $i > $i ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_FuncSet_Oextensional_decl,type,
c_FuncSet_Oextensional: $i > $i > $i > $i ).
thf(c_List_Obutlast_decl,type,
c_List_Obutlast: $i > $i > $i ).
thf(c_List_Odistinct_decl,type,
c_List_Odistinct: $i > $i > $o ).
thf(c_List_OtakeWhile_decl,type,
c_List_OtakeWhile: $i > $i > $i > $i ).
thf(c_List_Olists_decl,type,
c_List_Olists: $i > $i > $i ).
thf(c_Relation_Osingle__valued_decl,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(c_List_Oinsert_decl,type,
c_List_Oinsert: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OIIA_decl,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
thf(v_F_decl,type,
v_F: $i ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_FuncSet_Orestrict_decl,type,
c_FuncSet_Orestrict: $i > $i > $i > $i > $i ).
thf(c_List_Olist_Olist__case_decl,type,
c_List_Olist_Olist__case: $i > $i > $i > $i > $i > $i ).
thf(c_Hilbert__Choice_Oinv__into_decl,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(c_Relation_ORange_decl,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Wellfounded_Oaccp_decl,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(c_Product__Type_Ointernal__split_decl,type,
c_Product__Type_Ointernal__split: $i > $i > $i > $i ).
thf(c_Product__Type_Oprod_Oprod__case_decl,type,
c_Product__Type_Oprod_Oprod__case: $i > $i > $i > $i ).
thf(c_FuncSet_Ocompose_decl,type,
c_FuncSet_Ocompose: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Ounanimity_decl,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
thf(c_List_Omaps_decl,type,
c_List_Omaps: $i > $i > $i > $i > $i ).
thf(c_COMBI_decl,type,
c_COMBI: $i > $i ).
thf(c_List_Olexord_decl,type,
c_List_Olexord: $i > $i > $i ).
thf(c_Hilbert__Choice_OEps_decl,type,
c_Hilbert__Choice_OEps: $i > $i > $i ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i ).
thf(c_fequal_decl,type,
c_fequal: $i ).
thf(c_Wellfounded_Oacc_decl,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OLin_decl,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(c_Wellfounded_Olex__prod_decl,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_List_Oappend_decl,type,
c_List_Oappend: $i > $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oindi_decl,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OProf_decl,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
thf(c_fNot_decl,type,
c_fNot: $i ).
thf(c_List_Olast_decl,type,
c_List_Olast: $i > $i > $i ).
thf(c_Recdef_Ocut_decl,type,
c_Recdef_Ocut: $i > $i > $i ).
thf(c_Product__Type_Ocurry_decl,type,
c_Product__Type_Ocurry: $i > $i > $i > $i > $i ).
thf(c_Recdef_Oadm__wf_decl,type,
c_Recdef_Oadm__wf: $i > $i > $i > $i > $o ).
thf(c_COMBS_decl,type,
c_COMBS: $i > $i > $i > $i ).
thf(c_Wellfounded_Omlex__prod_decl,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(c_Predicate_ODomainP_decl,type,
c_Predicate_ODomainP: $i > $i > $i > $i > $o ).
thf(c_List_Omeasures_decl,type,
c_List_Omeasures: $i > $i > $i ).
thf(c_List_Olex_decl,type,
c_List_Olex: $i > $i > $i ).
thf(c_HOL_Oundefined_decl,type,
c_HOL_Oundefined: $i > $i ).
thf(c_Arrow__Order__Mirabelle_Oabove_decl,type,
c_Arrow__Order__Mirabelle_Oabove: $i > $i > $i > $i ).
thf(c_Relation_Oirrefl_decl,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(c_Arrow__Order__Mirabelle_Omktop_decl,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(c_fconj_decl,type,
c_fconj: $i ).
thf(c_Arrow__Order__Mirabelle_Omkbot_decl,type,
c_Arrow__Order__Mirabelle_Omkbot: $i > $i > $i ).
thf(c_Fun_Ooverride__on_decl,type,
c_Fun_Ooverride__on: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Predicate_ORangeP_decl,type,
c_Predicate_ORangeP: $i > $i > $i > $i > $o ).
thf(c_List_Opartition_decl,type,
c_List_Opartition: $i > $i > $i > $i ).
thf(c_If_decl,type,
c_If: $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Odictator_decl,type,
c_Arrow__Order__Mirabelle_Odictator: $i > $i > $o ).
thf(v_P_H_____decl,type,
v_P_H____: $i ).
thf(c_Product__Type_Oprod_Oprod__rec_decl,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Wellfounded_Omeasure_decl,type,
c_Wellfounded_Omeasure: $i > $i > $i ).
thf(c_List_Olexn_decl,type,
c_List_Olexn: $i > $i > $i > $i ).
thf(c_Nitpick_Orefl_H_decl,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(c_FunDef_Oin__rel_decl,type,
c_FunDef_Oin__rel: $i > $i > $i > $i > $i > $o ).
thf(c_Recdef_Osame__fst_decl,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( A @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb) ).
thf(892,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__fun__def) ).
thf(2094,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) ) @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__mem) ).
thf(1469,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) ) @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(518,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(2744,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(301,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) )
= ( A @ ( c_fequal @ ( c_fconj @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ c_COMBC ) ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__def_H) ).
thf(1633,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) )
= ( A @ ( c_fequal @ ( c_fconj @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ c_COMBC ) ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(1105,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olists ) @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__in__lists__conv) ).
thf(2412,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ c_List_Olists ) @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( D @ ( B @ ( E @ c_FuncSet_OPi ) ) ) @ ( A @ ( C @ ( B @ ( E @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( B @ ( E @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
thf(909,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( D @ ( B @ ( E @ c_FuncSet_OPi ) ) ) @ ( A @ ( C @ ( B @ ( E @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( B @ ( E @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( F @ ( G @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ! [H: $i,I: $i] :
( ( A @ ( I @ ( H @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( F @ ( G @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( I @ ( H @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).
thf(2499,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( F @ ( G @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
!= ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ! [H: $i,I: $i] :
( ( A @ ( I @ ( H @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( F @ ( G @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( I @ ( H @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ ( F @ ( G @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityE) ).
thf(777,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
thf(1818,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
<=> ( ? [F: $i] :
( ( ( C @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
& ( D
= ( F @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( ( C
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
& ( D
= ( E @ c_List_Olist_ONil ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__Cons__conv) ).
thf(1549,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ? [F: $i] :
( ( ( C @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
& ( D
= ( F @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( ( C
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
& ( D
= ( E @ c_List_Olist_ONil ) ) ) )
=> ( ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ? [F: $i] :
( ( ( C @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
& ( D
= ( F @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( ( C
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
& ( D
= ( E @ c_List_Olist_ONil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
<=> ( B
= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv2) ).
thf(2280,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B
= ( C @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ) )
& ( ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
=> ( B
= ( C @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olex ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil2__notin__lex) ).
thf(1686,plain,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olex ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(352,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Relation_Otrans ) )
=> ( ( A @ ( C @ c_Relation_Otrans ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Relation_Otrans ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Int) ).
thf(1879,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Relation_Otrans ) )
=> ( ( A @ ( C @ c_Relation_Otrans ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Relation_Otrans ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olistrel1 ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__listrel1__Nil) ).
thf(1337,plain,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olistrel1 ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__mono) ).
thf(760,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(448,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).
thf(2341,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ c_Relation_ORange ) ) @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeI) ).
thf(2336,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ c_Relation_ORange ) ) @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) )
<=> ( ( A
= ( C @ c_List_Olist_ONil ) )
& ( B
= ( C @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__is__Nil__conv) ).
thf(2031,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A
= ( C @ c_List_Olist_ONil ) )
& ( B
= ( C @ c_List_Olist_ONil ) ) )
=> ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( C @ c_List_Olist_ONil ) )
=> ( ( A
= ( C @ c_List_Olist_ONil ) )
& ( B
= ( C @ c_List_Olist_ONil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_Ocurry ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__split) ).
thf(2427,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_Ocurry ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(374,axiom,
c_Arrow__Order__Mirabelle_OProf @ ( v_c____ @ ( v_a____ @ ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( v_P____ @ ( c_Arrow__Order__Mirabelle_Obelow @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_058_AProf_096) ).
thf(1982,plain,
c_Arrow__Order__Mirabelle_OProf @ ( v_c____ @ ( v_a____ @ ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( v_P____ @ ( c_Arrow__Order__Mirabelle_Obelow @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( C @ ( A @ ( B @ ( F @ ( D @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_FuncSet_Orestrict ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__def) ).
thf(1855,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( C @ ( A @ ( B @ ( F @ ( D @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_FuncSet_Orestrict ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) @ ( B @ ( B @ c_Relation_ODomain ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
thf(762,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) @ ( B @ ( B @ c_Relation_ODomain ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(1406,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ? [D: $i,E: $i] :
( ( A @ ( C @ c_List_Olists ) @ ( E @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( E @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( B
= ( C @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists_Osimps) ).
thf(1443,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ? [D: $i,E: $i] :
( ( A @ ( C @ c_List_Olists ) @ ( E @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( E @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( B
= ( C @ c_List_Olist_ONil ) ) )
=> ( A @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ? [D: $i,E: $i] :
( ( A @ ( C @ c_List_Olists ) @ ( E @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B
= ( E @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( B
= ( C @ c_List_Olist_ONil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( c_fequal @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Hilbert__Choice_OEps ) )
= ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Eps__split__eq) ).
thf(2590,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( c_fequal @ hAPP ) @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( D @ tc_prod ) @ c_Hilbert__Choice_OEps ) )
= ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
thf(1422,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
thf(741,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__append__eq) ).
thf(1205,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(400,axiom,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mktop__Lin) ).
thf(2114,plain,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_ODomainP ) ) ) )
<=> ( B @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).
thf(1437,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_ODomainP ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_ODomainP ) ) ) )
=> ( B @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(861,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A != B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__subset) ).
thf(1173,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubsetD) ).
thf(2099,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Oirrefl ) )
<=> ! [C: $i] :
~ ( A @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__def) ).
thf(1591,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( A @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Relation_Oirrefl ) ) )
& ( ( A @ ( B @ c_Relation_Oirrefl ) )
=> ! [C: $i] :
~ ( A @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(655,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_List_Olistsp ) )
= ( A @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__Int__eq) ).
thf(2380,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_List_Olistsp ) )
= ( A @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( G @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( C @ ( E @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( F = D ) )
| ( B @ ( D @ ( F @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lex__prod) ).
thf(1137,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( ( ( A @ ( C @ ( E @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( F = D ) )
| ( B @ ( D @ ( F @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( G @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( G @ ( H @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( C @ ( E @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( F = D ) )
| ( B @ ( D @ ( F @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I_H) ).
thf(1327,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryI) ).
thf(1260,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( E @ ( tc_HOL_Obool @ ( C @ ( D @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
thf(2459,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(407,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Opartition ) ) )
= ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition_Osimps_I1_J) ).
thf(2146,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Opartition ) ) )
= ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( G @ ( K @ ( tc_HOL_Obool @ ( J @ tc_fun ) @ c_COMBK ) ) @ ( H @ ( J @ ( K @ c_FuncSet_OPi ) ) ) @ ( I @ ( J @ ( K @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( J @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) ) @ ( G @ ( F @ ( J @ c_FuncSet_OPi ) ) ) @ ( E @ ( F @ ( J @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( D @ ( C @ ( F @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( I @ ( E @ ( H @ ( F @ ( J @ ( K @ c_FuncSet_Ocompose ) ) ) ) ) @ ( B @ ( H @ ( C @ ( F @ ( K @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( I @ ( E @ ( B @ ( G @ ( C @ ( F @ ( J @ c_FuncSet_Ocompose ) ) ) ) ) @ ( H @ ( C @ ( J @ ( K @ c_FuncSet_Ocompose ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__assoc) ).
thf(1458,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( G @ ( K @ ( tc_HOL_Obool @ ( J @ tc_fun ) @ c_COMBK ) ) @ ( H @ ( J @ ( K @ c_FuncSet_OPi ) ) ) @ ( I @ ( J @ ( K @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( J @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) ) @ ( G @ ( F @ ( J @ c_FuncSet_OPi ) ) ) @ ( E @ ( F @ ( J @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( D @ ( C @ ( F @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( I @ ( E @ ( H @ ( F @ ( J @ ( K @ c_FuncSet_Ocompose ) ) ) ) ) @ ( B @ ( H @ ( C @ ( F @ ( K @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( I @ ( E @ ( B @ ( G @ ( C @ ( F @ ( J @ c_FuncSet_Ocompose ) ) ) ) ) @ ( H @ ( C @ ( J @ ( K @ c_FuncSet_Ocompose ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(2195,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( A @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( A @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__acc__listrel1I) ).
thf(1705,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( A @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( A @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(199,axiom,
c_Arrow__Order__Mirabelle_OProf @ ( v_b____ @ ( v_c____ @ ( v_P____ @ ( c_Arrow__Order__Mirabelle_Obelow @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096) ).
thf(1164,plain,
c_Arrow__Order__Mirabelle_OProf @ ( v_b____ @ ( v_c____ @ ( v_P____ @ ( c_Arrow__Order__Mirabelle_Obelow @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
thf(797,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
!= ( C @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).
thf(2434,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
!= ( C @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(349,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Relation_Otrans ) )
=> ( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( C @ ( B @ ( D @ c_Wellfounded_Olex__prod ) ) ) @ ( B @ ( D @ tc_prod ) @ c_Relation_Otrans ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__lex__prod) ).
thf(1872,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Relation_Otrans ) )
=> ( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( C @ ( B @ ( D @ c_Wellfounded_Olex__prod ) ) ) @ ( B @ ( D @ tc_prod ) @ c_Relation_Otrans ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(670,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E = F ) ) )
=> ( A @ ( B @ ( C @ c_Relation_Osingle__valued ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedI) ).
thf(2575,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E = F ) ) )
=> ( A @ ( B @ ( C @ c_Relation_Osingle__valued ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(326,axiom,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
thf(1746,plain,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Oinject) ).
thf(1782,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower2) ).
thf(841,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__mono) ).
thf(1046,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__lesseq) ).
thf(1482,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
thf(651,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olexord ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [D: $i,E: $i] :
( B
= ( E @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__Nil__left) ).
thf(2173,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i,E: $i] :
( B
= ( E @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( A @ ( C @ c_List_Olexord ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_List_Olexord ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i,E: $i] :
( B
= ( E @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__idem) ).
thf(565,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Relation_OId__on ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [D: $i] :
( ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
!= ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__onE) ).
thf(1628,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Relation_OId__on ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [D: $i] :
( ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
!= ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
thf(724,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(1287,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oidem) ).
thf(570,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mkbot) ).
thf(1792,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) )
=> ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(516,axiom,
! [A: $i] :
( ( A @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( v_P_H____ @ hAPP ) @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iff) ).
thf(2735,plain,
! [A: $i] :
( ( ( A @ ( v_P_H____ @ hAPP ) @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_P_H____ @ hAPP ) @ ( v_a____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(785,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olistrel1 ) @ ( E @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olistrel1 ) @ ( E @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).
thf(1323,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olistrel1 ) @ ( E @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olistrel1 ) @ ( E @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(434,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
thf(2274,plain,
v_a____ != v_b____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(2185,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_Oextensional__funcset ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ hAPP ) )
= ( E @ c_HOL_Oundefined ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__arb) ).
thf(2562,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_Oextensional__funcset ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ hAPP ) )
= ( E @ c_HOL_Oundefined ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( E @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__less) ).
thf(1832,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( E @ ( tc_Nat_Onat @ ( B @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Omeasures ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
thf(1992,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( F @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(136,axiom,
v_F @ c_Arrow__Order__Mirabelle_OIIA,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I3_J) ).
thf(949,plain,
v_F @ c_Arrow__Order__Mirabelle_OIIA,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ c_List_Olist_ONil @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( E @ c_List_Olist_ONil @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append1__eq__conv) ).
thf(1760,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( E @ c_List_Olist_ONil @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( E @ c_List_Olist_ONil @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( ( E @ c_List_Olist_ONil @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( E @ c_List_Olist_ONil @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Relation_OId__on ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
thf(1298,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Relation_OId__on ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Osimps_I2_J) ).
thf(1264,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
thf(2217,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olexord ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__Nil__right) ).
thf(1313,plain,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olexord ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(218,axiom,
c_Arrow__Order__Mirabelle_OLin @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) ) @ ( c_Arrow__Order__Mirabelle_OProf @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_FuncSet_OPi ) ) ) @ ( v_F @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I1_J) ).
thf(1279,plain,
c_Arrow__Order__Mirabelle_OLin @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) ) @ ( c_Arrow__Order__Mirabelle_OProf @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_FuncSet_OPi ) ) ) @ ( v_F @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(540,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(541,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( C @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[540]) ).
thf(542,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ~ ( C @ class_Orderings_Olinorder )
| ( B = A ) ),
inference(lifteq,[status(thm)],[541]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( C @ ( E @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mono) ).
thf(2703,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( C @ ( E @ tc_fun ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ c_Relation_ODomain ) ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainI) ).
thf(1379,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ c_Relation_ODomain ) ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(275,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olistrel ) @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel_ONil) ).
thf(1514,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olistrel ) @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(486,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Arrow__Order__Mirabelle_Odictator ) )
<=> ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictator__def) ).
thf(2552,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) )
=> ( A @ ( B @ c_Arrow__Order__Mirabelle_Odictator ) ) )
& ( ( A @ ( B @ c_Arrow__Order__Mirabelle_Odictator ) )
=> ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__iff) ).
thf(1890,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower1) ).
thf(969,plain,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(156,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olistrel1 ) @ ( B @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ c_List_Olistrel ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).
thf(1013,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olistrel1 ) @ ( B @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ c_List_Olistrel ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downward) ).
thf(1398,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D1) ).
thf(1115,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_COMBI @ ( D @ ( D @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( D @ ( D @ ( E @ c_FuncSet_Ocompose ) ) ) ) ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__compose) ).
thf(1815,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_COMBI @ ( D @ ( D @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( D @ ( D @ ( E @ c_FuncSet_Ocompose ) ) ) ) ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__IntI) ).
thf(1778,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( F @ c_List_Olexord ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( F @ c_List_Olexord ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__cons__cons) ).
thf(2388,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ( A @ ( F @ c_List_Olexord ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( F @ c_List_Olexord ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( F @ c_List_Olexord ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( F @ c_List_Olexord ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(1100,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( C @ ( B @ c_List_Obutlast ) @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( A @ ( B @ c_List_Obutlast ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__append) ).
thf(2713,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( C @ ( B @ c_List_Obutlast ) @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( A @ ( B @ c_List_Obutlast ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(638,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_List_Olistrel ) )
= ( A @ ( B @ c_List_Olistrel1 ) @ ( B @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).
thf(853,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_List_Olistrel ) )
= ( A @ ( B @ c_List_Olistrel1 ) @ ( B @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(367,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olistrel ) @ ( B @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i,G: $i] :
( ( D
= ( G @ ( F @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( E @ c_List_Olistrel ) @ ( B @ ( G @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons2) ).
thf(1931,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olistrel ) @ ( B @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i,G: $i] :
( ( D
= ( G @ ( F @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( E @ c_List_Olistrel ) @ ( B @ ( G @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ ( B @ ( E @ ( C @ ( D @ ( G @ c_FuncSet_Ocompose ) ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__eq) ).
thf(1568,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ ( B @ ( E @ ( C @ ( D @ ( G @ c_FuncSet_Ocompose ) ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i] :
~ ( tc_Nat_Onat @ ( C @ tc_fun ) @ c_List_Olist_ONil @ ( C @ c_List_Omeasures ) @ ( A @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measures_I1_J) ).
thf(2520,plain,
! [A: $i,B: $i,C: $i] :
~ ( tc_Nat_Onat @ ( C @ tc_fun ) @ c_List_Olist_ONil @ ( C @ c_List_Omeasures ) @ ( A @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F @ ( G @ hAPP ) @ hBOOL )
=> ( ( F @ ( B @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( G @ ( E @ ( A @ c_Recdef_Osame__fst ) ) ) @ ( C @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__fstI) ).
thf(2730,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( F @ ( G @ hAPP ) @ hBOOL )
=> ( ( F @ ( B @ hAPP ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( G @ ( E @ ( A @ c_Recdef_Osame__fst ) ) ) @ ( C @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ ( E @ ( A @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( A @ tc_prod ) @ ( E @ ( A @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_COMBK ) ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(2456,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_COMBK ) ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [I: $i,J: $i] :
( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( J @ ( I @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [K: $i,L: $i] :
( ( B @ ( L @ ( K @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( J @ ( I @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( J @ ( I @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( L @ ( K @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).
thf(1302,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [I: $i,J: $i] :
( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( J @ ( I @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [K: $i,L: $i] :
( ( B @ ( L @ ( K @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( J @ ( I @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( J @ ( I @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( L @ ( K @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
thf(789,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(591,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__commute) ).
thf(646,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).
thf(834,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_Wellfounded_Oacc ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards) ).
thf(1151,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_Wellfounded_Oacc ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olistrel1 ) @ ( B @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( D
= ( B @ ( F @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ~ ( A @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ! [F: $i] :
( ( D
= ( F @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ~ ( A @ ( E @ c_List_Olistrel1 ) @ ( B @ ( F @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__listrel1E2) ).
thf(2291,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olistrel1 ) @ ( B @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( D
= ( B @ ( F @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ~ ( A @ ( C @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ! [F: $i] :
( ( D
= ( F @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ~ ( A @ ( E @ c_List_Olistrel1 ) @ ( B @ ( F @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_List_Olistsp ) )
= ( A @ ( C @ c_List_Olistsp ) @ ( B @ ( C @ c_List_Olistsp ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__inf__eq) ).
thf(821,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_List_Olistsp ) )
= ( A @ ( C @ c_List_Olistsp ) @ ( B @ ( C @ c_List_Olistsp ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(905,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Wellfounded_Oacc ) @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Olistrel1 ) @ ( C @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__accD) ).
thf(1714,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Wellfounded_Oacc ) @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_List_Olistrel1 ) @ ( C @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( A @ ( B @ ( C @ ( D @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__extensional) ).
thf(2027,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( A @ ( B @ ( C @ ( D @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
thf(1040,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(525,plain,
~ ! [A: $i] :
( ( ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(526,plain,
~ ( ! [A: $i] :
( ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ! [A: $i] :
( ( A @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(miniscope,[status(thm)],[525]) ).
thf(527,plain,
( ( ~ ( sk2 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( v_b____ @ ( v_c____ @ ( sk1 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( v_b____ @ ( v_c____ @ ( sk1 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( sk2 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(cnf,[status(esa)],[526]) ).
thf(528,plain,
( ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(cnfConj,[status(thm)],[527]) ).
thf(529,plain,
( ~ ( sk2 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(cnfConj,[status(thm)],[527]) ).
thf(2776,plain,
( ( ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
!= ( sk2 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
| ~ $true
| ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[528,529]) ).
thf(2777,plain,
( ( ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
!= ( sk2 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[2776]) ).
thf(2779,plain,
( ( ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) )
!= ( sk2 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) ) )
| ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[2777]) ).
thf(2806,plain,
( ( ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) )
!= ( sk2 @ ( v_P____ @ hAPP ) ) )
| ( ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) )
!= ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) ) )
| ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[2779]) ).
thf(2815,plain,
( ( sk2 != v_b____ )
| ( ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) )
!= v_P____ )
| ( ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
!= ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
| ( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member )
!= ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member ) )
| ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[2806]) ).
thf(2893,plain,
( ( sk2 != v_b____ )
| ( ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) )
!= v_P____ )
| ( ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
!= ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
| ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[2815]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(2469,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Olistrelp ) ) ) )
<=> ( ( A @ ( C @ ( E @ ( F @ c_List_Olistrelp ) ) ) )
& ( B @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_Oequations_I2_J) ).
thf(1858,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( A @ ( C @ ( E @ ( F @ c_List_Olistrelp ) ) ) )
& ( B @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Olistrelp ) ) ) ) )
& ( ( A @ ( B @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Olistrelp ) ) ) )
=> ( ( A @ ( C @ ( E @ ( F @ c_List_Olistrelp ) ) ) )
& ( B @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).
thf(2122,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(2894,plain,
( ( sk2 != v_b____ )
| ( ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) )
!= v_P____ )
| ( v_c____ != v_b____ )
| ( ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) )
!= ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) ) )
| ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[2893]) ).
thf(2917,plain,
( ( sk2 != v_b____ )
| ( ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) )
!= v_P____ )
| ( v_c____ != v_b____ )
| ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[2894]) ).
thf(489,axiom,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(2567,plain,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(2568,plain,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL ) ),
inference(cnf,[status(esa)],[2567]) ).
thf(4658,plain,
! [A: $i] :
( ( ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
!= ( A @ hBOOL ) )
| ~ $true
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ( sk2 != v_b____ )
| ( ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) )
!= v_P____ )
| ( v_c____ != v_b____ ) ),
inference(paramod_ordered,[status(thm)],[2917,2568]) ).
thf(4659,plain,
! [A: $i] :
( ( ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
!= ( A @ hBOOL ) )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ( sk2 != v_b____ )
| ( ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) )
!= v_P____ )
| ( v_c____ != v_b____ ) ),
inference(simp,[status(thm)],[4658]) ).
thf(4660,plain,
( ~ ( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ ( c_fNot @ hAPP ) @ hBOOL )
| ( sk2 != v_b____ )
| ( ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) )
!= v_P____ )
| ( v_c____ != v_b____ ) ),
inference(pattern_uni,[status(thm)],[4659:[bind(A,$thf( sk1 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) ))]]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiE) ).
thf(1377,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(634,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Osemilattice__inf )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__mono) ).
thf(734,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Osemilattice__inf )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
thf(1886,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Osplice ) ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I2_J) ).
thf(2523,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Osplice ) ) )
= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
thf(1622,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
thf(1394,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ c_HOL_Oundefined ) ) )
& ( ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut__def) ).
thf(1526,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ c_HOL_Oundefined ) ) )
& ( ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(47,axiom,
tc_HOL_Obool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(662,plain,
tc_HOL_Obool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(536,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B != A )
| ~ ( C @ class_Orderings_Opreorder ) ),
inference(cnf,[status(esa)],[536]) ).
thf(538,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( C @ class_Orderings_Opreorder )
| ( B != A ) ),
inference(lifteq,[status(thm)],[537]) ).
thf(539,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( B @ class_Orderings_Opreorder ) ),
inference(simp,[status(thm)],[538]) ).
thf(2807,plain,
! [B: $i,A: $i] :
( ( ( tc_HOL_Obool @ class_Orderings_Opreorder )
!= ( B @ class_Orderings_Opreorder ) )
| ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[662,539]) ).
thf(2808,plain,
! [B: $i,A: $i] :
( ( ( tc_HOL_Obool @ class_Orderings_Opreorder )
!= ( B @ class_Orderings_Opreorder ) )
| ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(simp,[status(thm)],[2807]) ).
thf(2809,plain,
! [A: $i] : ( A @ ( A @ ( tc_HOL_Obool @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(pattern_uni,[status(thm)],[2808:[bind(A,$thf( A )),bind(B,$thf( tc_HOL_Obool ))]]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_OaccI) ).
thf(1433,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(183,axiom,
tc_Nat_Onat @ class_Lattices_Olattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
thf(1104,plain,
tc_Nat_Onat @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Omaps ) ) ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omaps ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_maps__simps_I1_J) ).
thf(1521,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Omaps ) ) ) )
= ( A @ ( C @ ( D @ ( E @ c_List_Omaps ) ) ) @ ( B @ ( C @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(476,axiom,
c_Arrow__Order__Mirabelle_OProf @ ( v_P____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096P_A_058_AProf_096) ).
thf(2508,plain,
c_Arrow__Order__Mirabelle_OProf @ ( v_P____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb1) ).
thf(981,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ c_List_Olist_ONil )
= ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ( ( A
= ( C @ c_List_Olist_ONil ) )
& ( B
= ( C @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__is__append__conv) ).
thf(2367,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A
= ( C @ c_List_Olist_ONil ) )
& ( B
= ( C @ c_List_Olist_ONil ) ) )
=> ( ( C @ c_List_Olist_ONil )
= ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ c_List_Olist_ONil )
= ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( A
= ( C @ c_List_Olist_ONil ) )
& ( B
= ( C @ c_List_Olist_ONil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D2) ).
thf(1928,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) )
= B )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( F @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).
thf(988,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) )
= B )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ ( C @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( F @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olistrel1 ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olistrel1 ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I2) ).
thf(2639,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olistrel1 ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olistrel1 ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(396,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut__apply) ).
thf(2103,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D
= ( B @ ( G @ ( H @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( H @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( A
= ( B @ ( F @ ( H @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( H @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( E @ ( H @ c_List_Olistrel1 ) @ ( A @ ( D @ ( H @ tc_List_Olist @ ( H @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ tc_List_Olist @ ( H @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I) ).
thf(2750,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D
= ( B @ ( G @ ( H @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( H @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( A
= ( B @ ( F @ ( H @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( H @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( E @ ( H @ c_List_Olistrel1 ) @ ( A @ ( D @ ( H @ tc_List_Olist @ ( H @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( H @ tc_List_Olist @ ( H @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb1) ).
thf(920,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD1) ).
thf(942,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( B @ c_HOL_Oundefined ) ) )
& ( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__def) ).
thf(2204,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( B @ c_HOL_Oundefined ) ) )
& ( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(1153,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Osplice ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I1_J) ).
thf(810,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Osplice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__above) ).
thf(2047,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) )
=> ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(226,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( B @ ( B @ c_FuncSet_OPi ) ) ) @ ( B @ c_COMBI @ ( B @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__id) ).
thf(1311,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( B @ ( B @ c_FuncSet_OPi ) ) ) @ ( B @ c_COMBI @ ( B @ ( B @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C1_C) ).
thf(2641,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(2083,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( A @ ( c_fequal @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
thf(714,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).
thf(1636,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ? [F: $i] :
( ( D
= ( F @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) ) )
& ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__image__iff) ).
thf(1057,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( D
= ( F @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) ) )
& ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ? [F: $i] :
( ( D
= ( F @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) ) )
& ( A @ ( F @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olists ) @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__in__lists__iff) ).
thf(1691,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ c_List_Olists ) @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_List_Olists ) @ ( B @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(546,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
thf(793,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(451,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ? [C: $i] : ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_third__alt) ).
thf(2364,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ? [C: $i] : ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( B @ hAPP ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
thf(2164,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( B @ hAPP ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
thf(1387,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD2) ).
thf(957,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(746,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( C = B ) )
& ( ( C = B )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( A @ ( B @ ( C @ ( D @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( D @ c_Set_Oimage ) ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__restrict__eq) ).
thf(952,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( A @ ( B @ ( C @ ( D @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( D @ c_Set_Oimage ) ) ) )
= ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olistrel1 ) @ ( C @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__accI) ).
thf(1123,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olistrel1 ) @ ( C @ tc_List_Olist @ c_Wellfounded_Oacc ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( C @ c_List_Olists ) @ ( B @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( C @ ( B @ c_List_Obutlast ) @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( B @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast_Osimps_I2_J) ).
thf(1487,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( C @ ( B @ c_List_Obutlast ) @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Obutlast ) )
= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(693,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(2606,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B )
<=> ( A
= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv) ).
thf(1824,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( C @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B ) )
& ( ( ( A @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B )
=> ( A
= ( C @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(435,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ ( C @ ( F @ c_Fun_Ooverride__on ) ) ) ) ) )
= ( E @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__apply__notin) ).
thf(2277,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ ( C @ ( F @ c_Fun_Ooverride__on ) ) ) ) ) )
= ( E @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mem) ).
thf(1355,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__ConsR) ).
thf(1580,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( B @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).
thf(1676,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( B @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olexord ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_List_Olexord ) @ ( A @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Relation_Otrans ) )
=> ( B @ ( E @ c_List_Olexord ) @ ( A @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__trans) ).
thf(2133,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olexord ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_List_Olexord ) @ ( A @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Relation_Otrans ) )
=> ( B @ ( E @ c_List_Olexord ) @ ( A @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__trans) ).
thf(916,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(369,axiom,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) ) @ ( c_Arrow__Order__Mirabelle_OProf @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_FuncSet_OPi ) ) ) @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( D != E )
=> ( ( A @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( A @ ( B @ c_Arrow__Order__Mirabelle_Odictator ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictatorI) ).
thf(1938,plain,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ c_COMBK ) ) @ ( c_Arrow__Order__Mirabelle_OProf @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_FuncSet_OPi ) ) ) @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ( D != E )
=> ( ( A @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( A @ ( B @ c_Arrow__Order__Mirabelle_Odictator ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__commute) ).
thf(1032,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Opartition ) ) )
= ( A @ ( C @ ( D @ c_List_Opartition ) ) @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ c_COMBB ) ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_If ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ c_COMBS ) ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition_Osimps_I2_J) ).
thf(1920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Opartition ) ) )
= ( A @ ( C @ ( D @ c_List_Opartition ) ) @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ c_COMBB ) ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_If ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ c_COMBS ) ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ ( D @ tc_List_Olist @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ tc_fun ) @ ( D @ tc_List_Olist @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Orotate1 ) )
= ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( D @ c_List_Olist_ONil @ ( D @ c_List_Orotate1 ) )
= ( D @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__simps) ).
thf(2477,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ c_List_Orotate1 ) )
= ( C @ c_List_Olist_ONil @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( D @ c_List_Olist_ONil @ ( D @ c_List_Orotate1 ) )
= ( D @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ hAPP ) @ hBOOL )
=> ( C @ ( A @ c_Hilbert__Choice_OEps ) @ ( C @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI) ).
thf(2565,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ hAPP ) @ hBOOL )
=> ( C @ ( A @ c_Hilbert__Choice_OEps ) @ ( C @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__mp) ).
thf(2332,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( D @ ( C @ c_Relation_ORange ) ) @ ( B @ ( D @ ( C @ c_Relation_ORange ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ ( C @ c_Relation_ORange ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Int__subset) ).
thf(1178,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( D @ ( C @ c_Relation_ORange ) ) @ ( B @ ( D @ ( C @ c_Relation_ORange ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ ( C @ c_Relation_ORange ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__image) ).
thf(1888,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oassoc) ).
thf(583,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( D @ ( E @ hAPP ) ) )
=> ( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( F @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).
thf(2181,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( D @ ( E @ hAPP ) ) )
=> ( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( F @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Product__Type_OPair ) @ ( A @ ( C @ ( B @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( B @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__eta) ).
thf(1656,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Product__Type_OPair ) @ ( A @ ( C @ ( B @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( B @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__takeWhile__le) ).
thf(1079,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(517,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Obutlast ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__snoc) ).
thf(2741,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Obutlast ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
thf(1740,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(551,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__eq__len) ).
thf(1128,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__less) ).
thf(1392,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ ( C @ ( C @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( C @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ c_Wellfounded_Oacc ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__acc__eq) ).
thf(2228,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_Wellfounded_Oacc ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ ( C @ ( C @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( C @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( C @ c_Product__Type_OPair ) @ ( C @ ( C @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( C @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( C @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Wellfounded_Oacc ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(1291,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(60,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__rtrancl) ).
thf(710,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(289,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI__ex) ).
thf(1573,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
thf(974,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( B = A )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__conj__eq) ).
thf(1983,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( B @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( c_fconj @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(344,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(1851,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olistrel1 ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Nil__listrel1) ).
thf(2377,plain,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olistrel1 ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitI) ).
thf(1375,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(477,axiom,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistsp ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Oequations_I1_J) ).
thf(2509,plain,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistsp ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Olexn ) ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= A )
& ( ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexn__length) ).
thf(2537,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Olexn ) ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= A )
& ( ( D @ ( E @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(869,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ ( C @ ( F @ c_Fun_Ooverride__on ) ) ) ) ) )
= ( E @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__apply__in) ).
thf(1755,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ ( C @ ( F @ c_Fun_Ooverride__on ) ) ) ) ) )
= ( E @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Relation_Otrans ) )
=> ( ( D @ ( B @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transD) ).
thf(1118,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Relation_Otrans ) )
=> ( ( D @ ( B @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryD) ).
thf(2300,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(578,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( A @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( C @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) )
=> ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensionalityI) ).
thf(1534,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( A @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( C @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I) ).
thf(2685,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( C @ ( A @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_above__Lin) ).
thf(1540,plain,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( C @ ( A @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Product__Type_Ointernal__split ) ) )
= ( A @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__def) ).
thf(1006,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Product__Type_Ointernal__split ) ) )
= ( A @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ( ? [F: $i] :
( ( C
= ( A @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( F @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= B ) )
| ( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= A )
& ( B
= ( E @ c_List_Olist_ONil ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__append__conv) ).
thf(1659,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ? [F: $i] :
( ( C
= ( A @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( F @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= B ) )
| ( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= A )
& ( B
= ( E @ c_List_Olist_ONil ) ) ) )
=> ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ? [F: $i] :
( ( C
= ( A @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( F @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= B ) )
| ( ( ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= A )
& ( B
= ( E @ c_List_Olist_ONil ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_OtakeWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).
thf(933,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_OtakeWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B = A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(554,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( E @ ( G @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( D @ hAPP ) )
= ( G @ ( C @ hAPP ) ) ) )
=> ( ( A @ ( E @ ( B @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( B @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( E @ ( B @ ( F @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__cong) ).
thf(1461,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( E @ ( G @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( D @ hAPP ) )
= ( G @ ( C @ hAPP ) ) ) )
=> ( ( ( A @ ( E @ ( B @ ( F @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( B @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( E @ ( B @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( B @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ ( F @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( A @ ( B @ c_List_Olast ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__append) ).
thf(1424,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( A @ ( B @ c_List_Olast ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( E @ ( A @ ( B @ c_Predicate_ORangeP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
thf(1842,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( E @ ( A @ ( B @ c_Predicate_ORangeP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(368,axiom,
c_Arrow__Order__Mirabelle_OProf @ ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( v_P____ @ ( c_Arrow__Order__Mirabelle_Obelow @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096) ).
thf(1937,plain,
c_Arrow__Order__Mirabelle_OProf @ ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( v_P____ @ ( c_Arrow__Order__Mirabelle_Obelow @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oindi @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate1D) ).
thf(2666,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) ) )
=> ( ( D @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) ) @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) ) @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__injective) ).
thf(1644,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) ) )
=> ( ( D @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) ) @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( E @ ( F @ c_Set_Oimage ) ) ) @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(58,axiom,
tc_Nat_Onat @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(706,plain,
tc_Nat_Onat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
thf(1028,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).
thf(2023,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct ) )
=> ( B @ ( A @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__takeWhile) ).
thf(901,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct ) )
=> ( B @ ( A @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( B @ c_HOL_Oundefined ) ) )
& ( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__apply) ).
thf(2419,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( B @ c_HOL_Oundefined ) ) )
& ( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ c_Wellfounded_Oaccp ) @ ( A @ ( C @ c_Wellfounded_Oaccp ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__subset) ).
thf(997,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ c_Wellfounded_Oaccp ) @ ( A @ ( C @ c_Wellfounded_Oaccp ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Wellfounded_Omeasure ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measure) ).
thf(2304,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( D @ c_Wellfounded_Omeasure ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_Wellfounded_Omeasure ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( C @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(1131,plain,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( A @ ( C @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__append__conv) ).
thf(1974,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( B @ c_List_Olist_ONil ) )
=> ( C
= ( A @ ( C @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( A @ ( C @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( A
= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(2243,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(493,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Nitpick_Orefl_H ) )
<=> ! [C: $i] : ( A @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
thf(2581,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( A @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Nitpick_Orefl_H ) ) )
& ( ( A @ ( B @ c_Nitpick_Orefl_H ) )
=> ! [C: $i] : ( A @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__assoc) ).
thf(721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(371,axiom,
! [A: $i] :
( ( A @ c_Arrow__Order__Mirabelle_OIIA )
<=> ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( F @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( F @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IIA__def) ).
thf(1947,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( ( F @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( F @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( C @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) )
=> ( A @ c_Arrow__Order__Mirabelle_OIIA ) )
& ( ( A @ c_Arrow__Order__Mirabelle_OIIA )
=> ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( ( F @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( F @ ( B @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( C @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( C @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ ( E @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(350,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBK ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).
thf(1874,plain,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_COMBK ) ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mktop) ).
thf(1599,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) )
=> ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(522,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ c_Hilbert__Choice_OEps ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).
thf(2756,plain,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ c_Hilbert__Choice_OEps ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(622,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(837,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Oequations) ).
thf(2125,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__apply) ).
thf(1588,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
thf(984,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__commute) ).
thf(911,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(475,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(2505,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= A )
=> ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( A @ ( C @ ( B @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( E @ ( D @ c_FuncSet_Orestrict ) ) ) @ ( E @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__funcset) ).
thf(1333,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= A )
=> ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( A @ ( C @ ( B @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( E @ ( D @ c_FuncSet_Orestrict ) ) ) @ ( E @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
thf(938,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
!= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq__if__length__neq) ).
thf(805,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
!= ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( A @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) ) @ ( B @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Int__subset) ).
thf(1035,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( A @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) ) @ ( B @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( E @ ( D @ c_Set_Oimage ) ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI2) ).
thf(1026,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistrelp ) ) ) )
<=> ( C @ ( D @ c_List_Olistrel ) @ ( A @ ( B @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp__listrel__eq) ).
thf(2546,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_List_Olistrel ) @ ( A @ ( B @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistrelp ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ ( D @ ( D @ tc_prod ) @ c_member @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ ( D @ ( D @ tc_prod ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistrelp ) ) ) )
=> ( C @ ( D @ c_List_Olistrel ) @ ( A @ ( B @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(524,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ c_List_Olist_ONil @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
<=> ( ( ( A @ ( D @ c_List_Olast ) )
= B )
& ( ( A @ ( D @ c_List_Obutlast ) )
= C )
& ( A
!= ( D @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snoc__eq__iff__butlast) ).
thf(2761,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( A @ ( D @ c_List_Olast ) )
= B )
& ( ( A @ ( D @ c_List_Obutlast ) )
= C )
& ( A
!= ( D @ c_List_Olist_ONil ) ) )
=> ( ( D @ c_List_Olist_ONil @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ) )
& ( ( ( D @ c_List_Olist_ONil @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
=> ( ( ( A @ ( D @ c_List_Olast ) )
= B )
& ( ( A @ ( D @ c_List_Obutlast ) )
= C )
& ( A
!= ( D @ c_List_Olist_ONil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_OdropWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).
thf(765,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_OdropWhile ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( C @ ( E @ ( F @ c_FuncSet_Oextensional ) ) @ ( A @ ( B @ ( C @ ( E @ ( D @ ( F @ c_FuncSet_Ocompose ) ) ) ) ) @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__extensional) ).
thf(1712,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( C @ ( E @ ( F @ c_FuncSet_Oextensional ) ) @ ( A @ ( B @ ( C @ ( E @ ( D @ ( F @ c_FuncSet_Ocompose ) ) ) ) ) @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ c_List_Omaps ) ) ) )
= ( B @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_maps__simps_I2_J) ).
thf(1054,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ c_List_Omaps ) ) ) )
= ( B @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(530,plain,
( ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( v_b____ @ ( v_c____ @ ( sk1 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(cnfConj,[status(thm)],[527]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( F @ c_List_Olistrel1 ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( F @ c_List_Olistrel1 ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( D = B )
& ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__listrel1__Cons) ).
thf(2617,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ( A @ ( F @ c_List_Olistrel1 ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( D = B )
& ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( F @ c_List_Olistrel1 ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( F @ c_List_Olistrel1 ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( F @ c_List_Olistrel1 ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( D = B )
& ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( B @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__trans) ).
thf(773,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( B @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).
thf(586,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
~ ( A @ ( E @ ( C @ ( B @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainE) ).
thf(2338,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
~ ( A @ ( E @ ( C @ ( B @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [E: $i] : ( A @ ( E @ ( C @ ( B @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__iff) ).
thf(1680,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( A @ ( E @ ( C @ ( B @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] : ( A @ ( E @ ( C @ ( B @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ c_List_Olist_ONil @ ( C @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( C @ hAPP ) @ hBOOL )
=> ( B @ c_List_Olist_ONil @ ( D @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__induct) ).
thf(1698,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ c_List_Olist_ONil @ ( C @ hAPP ) @ hBOOL )
=> ( ! [D: $i,E: $i] :
( ( E @ ( C @ hAPP ) @ hBOOL )
=> ( B @ c_List_Olist_ONil @ ( D @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_List_Olist_Olist__case ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I5_J) ).
thf(2149,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_List_Olist_Olist__case ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_FuncSet_Oextensional__funcset ) ) ) )
= ( B @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( C @ ( D @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__def) ).
thf(824,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_FuncSet_Oextensional__funcset ) ) ) )
= ( B @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( C @ ( D @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(105,axiom,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast_Osimps_I1_J) ).
thf(856,plain,
! [A: $i] :
( ( A @ c_List_Olist_ONil @ ( A @ c_List_Obutlast ) )
= ( A @ c_List_Olist_ONil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(573,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(323,axiom,
! [A: $i] :
( ( A @ c_Arrow__Order__Mirabelle_Ounanimity )
<=> ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unanimity__def) ).
thf(1727,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ c_Arrow__Order__Mirabelle_Ounanimity ) )
& ( ( A @ c_Arrow__Order__Mirabelle_Ounanimity )
=> ! [B: $i] :
( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ ( D @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C
= ( B @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__Nil__appendI) ).
thf(1510,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( C
= ( B @ ( A @ c_List_Olist_ONil @ ( A @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(118,axiom,
! [A: $i] : ( A @ c_List_Olist_ONil @ ( A @ c_List_Odistinct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).
thf(903,plain,
! [A: $i] : ( A @ c_List_Olist_ONil @ ( A @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(904,plain,
! [A: $i] : ( A @ c_List_Olist_ONil @ ( A @ c_List_Odistinct ) ),
inference(cnf,[status(esa)],[903]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D1) ).
thf(1389,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_OdropWhile ) ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
<=> ( ~ ( B @ ( D @ hAPP ) @ hBOOL )
& ( C
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_OtakeWhile ) ) @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).
thf(2489,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ~ ( B @ ( D @ hAPP ) @ hBOOL )
& ( C
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_OtakeWhile ) ) @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
=> ( ( C @ ( D @ ( E @ c_List_OdropWhile ) ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_List_OdropWhile ) ) )
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ~ ( B @ ( D @ hAPP ) @ hBOOL )
& ( C
= ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_OtakeWhile ) ) @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(743,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(253,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orotate1 ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Oappend @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ ( B @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Olist_ONil @ ( B @ ( B @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__def) ).
thf(1403,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orotate1 ) )
= ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_OCons @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Oappend @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ ( B @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_fun ) @ ( B @ tc_List_Olist @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( B @ c_List_Olist_ONil @ ( B @ ( B @ tc_List_Olist @ c_List_Olist_Olist__case ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(277,axiom,
tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( v_c____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Odistinct ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dist) ).
thf(1520,plain,
tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( v_c____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Odistinct ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(7,axiom,
tc_Nat_Onat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(545,plain,
tc_Nat_Onat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ ( C @ c_List_OtakeWhile ) ) )
= ( B @ ( E @ ( C @ c_List_OtakeWhile ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__tail) ).
thf(2225,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ ( C @ c_List_OtakeWhile ) ) )
= ( B @ ( E @ ( C @ c_List_OtakeWhile ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( E @ c_Relation_Osingle__valued ) ) )
=> ( ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
thf(1884,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ ( E @ c_Relation_Osingle__valued ) ) )
=> ( ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
thf(843,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitD) ).
thf(1125,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(875,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(18,axiom,
tc_HOL_Obool @ class_Lattices_Osemilattice__inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
thf(577,plain,
tc_HOL_Obool @ class_Lattices_Osemilattice__inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(711,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Relation_Otrans ) ),
inference(cnf,[status(esa)],[710]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(641,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olex ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__notin__lex) ).
thf(1503,plain,
! [A: $i,B: $i,C: $i] :
~ ( A @ ( C @ c_List_Olex ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(418,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( C @ c_List_Olistrel ) @ ( B @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__refl) ).
thf(2193,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( C @ c_List_Olistrel ) @ ( B @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(132,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olistrel1 ) @ ( B @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_List_Olistrel1 ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).
thf(936,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olistrel1 ) @ ( B @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_List_Olistrel1 ) @ ( tc_HOL_Obool @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1E) ).
thf(1707,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntE) ).
thf(1865,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(523,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( H @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBK ) ) @ ( E @ ( G @ ( H @ c_FuncSet_OPi ) ) ) @ ( F @ ( G @ ( H @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( G @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( D @ ( C @ ( G @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( H @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( E @ ( C @ ( H @ c_FuncSet_OPi ) ) ) @ ( F @ ( B @ ( E @ ( C @ ( G @ ( H @ c_FuncSet_Ocompose ) ) ) ) ) @ ( C @ ( H @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__compose) ).
thf(2759,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( H @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ c_COMBK ) ) @ ( E @ ( G @ ( H @ c_FuncSet_OPi ) ) ) @ ( F @ ( G @ ( H @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( G @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( D @ ( C @ ( G @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( G @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( H @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( E @ ( C @ ( H @ c_FuncSet_OPi ) ) ) @ ( F @ ( B @ ( E @ ( C @ ( G @ ( H @ c_FuncSet_Ocompose ) ) ) ) ) @ ( C @ ( H @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= A )
=> ( ( A @ ( C @ ( B @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( E @ ( D @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( A @ ( D @ ( E @ ( D @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( A @ ( D @ c_COMBI @ ( D @ ( D @ c_FuncSet_Orestrict ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__id__inv__into) ).
thf(1090,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) ) )
= A )
=> ( ( A @ ( C @ ( B @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( E @ ( D @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( A @ ( D @ ( E @ ( D @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( A @ ( D @ c_COMBI @ ( D @ ( D @ c_FuncSet_Orestrict ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
thf(704,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= C )
=> ( ( B
= ( A @ ( D @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__appendI) ).
thf(1638,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= C )
=> ( ( B
= ( A @ ( D @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( D @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1I) ).
thf(2029,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( D @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Predicate_ORangeP ) ) ) )
<=> ? [E: $i] : ( A @ ( E @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
thf(2326,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( A @ ( E @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ c_Predicate_ORangeP ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Predicate_ORangeP ) ) ) )
=> ? [E: $i] : ( A @ ( E @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(611,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(787,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__ConsL) ).
thf(1897,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(799,plain,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(800,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B != A ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(cnf,[status(esa)],[799]) ).
thf(802,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B != A ) ),
inference(cnfConj,[status(thm)],[800]) ).
thf(803,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( B != A ) ),
inference(lifteq,[status(thm)],[802]) ).
thf(804,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(simp,[status(thm)],[803]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ c_Wellfounded_Oacc ) @ ( A @ ( C @ c_Wellfounded_Oacc ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__subset) ).
thf(2573,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ c_Wellfounded_Oacc ) @ ( A @ ( C @ c_Wellfounded_Oacc ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i,G: $i] :
( ( B
= ( G @ ( F @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( E @ c_List_Olistrel ) @ ( G @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons1) ).
thf(2358,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i,G: $i] :
( ( B
= ( G @ ( F @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( ( A @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( E @ c_List_Olistrel ) @ ( G @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__idem) ).
thf(604,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C
!= ( B @ ( A @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_impossible__Cons) ).
thf(1194,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C
!= ( B @ ( A @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb2) ).
thf(831,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).
thf(681,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Ointernal__split ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__conv) ).
thf(2383,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Ointernal__split ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(155,axiom,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__refl) ).
thf(1011,plain,
! [A: $i,B: $i] : ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_Oextensional__funcset ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__mem) ).
thf(1524,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_Oextensional__funcset ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( A @ ( B @ c_Predicate_ODomainP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
thf(2097,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( A @ ( B @ c_Predicate_ODomainP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ? [F: $i] :
( ( ( C
= ( A @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( F @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B ) )
| ( ( ( C @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
& ( D
= ( F @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).
thf(2257,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( ( C
= ( A @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( F @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B ) )
| ( ( ( C @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
& ( D
= ( F @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) )
=> ( ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ? [F: $i] :
( ( ( C
= ( A @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
& ( ( F @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B ) )
| ( ( ( C @ ( F @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A )
& ( D
= ( F @ ( B @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).
thf(2246,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( B @ c_Relation_ORange ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [E: $i] : ( A @ ( C @ ( E @ ( D @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__iff) ).
thf(2116,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( A @ ( C @ ( E @ ( D @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_Relation_ORange ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ ( B @ c_Relation_ORange ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] : ( A @ ( C @ ( E @ ( D @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__into) ).
thf(1571,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( A @ ( E @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Odistinct ) )
=> ( ( B @ ( B @ ( A @ c_List_Olast ) @ ( c_fequal @ ( tc_HOL_Obool @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ c_List_OtakeWhile ) ) )
= ( B @ ( A @ c_List_Obutlast ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__not__last) ).
thf(1175,plain,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Odistinct ) )
=> ( ( B @ ( B @ ( A @ c_List_Olast ) @ ( c_fequal @ ( tc_HOL_Obool @ ( A @ ( A @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fNot @ ( A @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ c_List_OtakeWhile ) ) )
= ( B @ ( A @ c_List_Obutlast ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(1048,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(736,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(322,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transI) ).
thf(1722,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( F @ c_List_Olex ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( F @ c_List_Olex ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( ( D @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) )
& ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__in__lex) ).
thf(2669,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ( A @ ( F @ c_List_Olex ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( ( D @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) )
& ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( F @ c_List_Olex ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( F @ c_List_Olex ) @ ( B @ ( C @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( F @ c_List_Olex ) @ ( B @ ( D @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( ( D @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( F @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) )
& ( A @ ( C @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(649,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).
thf(1043,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__appendR) ).
thf(1471,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mono) ).
thf(2025,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Ocommute) ).
thf(631,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(71,axiom,
tc_HOL_Obool @ class_Lattices_Olattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
thf(758,plain,
tc_HOL_Obool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
<=> ( ? [D: $i,E: $i] :
( ( E @ ( B @ ( C @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ hAPP ) @ hBOOL )
& ( A
= ( E @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( A
= ( C @ c_List_Olist_ONil ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Osimps) ).
thf(2343,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ? [D: $i,E: $i] :
( ( E @ ( B @ ( C @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ hAPP ) @ hBOOL )
& ( A
= ( E @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( A
= ( C @ c_List_Olist_ONil ) ) )
=> ( A @ ( B @ ( C @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( ? [D: $i,E: $i] :
( ( E @ ( B @ ( C @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ hAPP ) @ hBOOL )
& ( A
= ( E @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
| ( A
= ( C @ c_List_Olist_ONil ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_List_Olistrel1 ) @ ( B @ ( C @ c_List_Olistrel1 ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__mono) ).
thf(816,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_List_Olistrel1 ) @ ( B @ ( C @ c_List_Olistrel1 ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__eq__len) ).
thf(2111,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_List_Olistrel ) @ ( B @ ( C @ c_List_Olistrel ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__mono) ).
thf(848,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_List_Olistrel ) @ ( B @ ( C @ c_List_Olistrel ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ c_COMBI @ ( B @ ( C @ ( D @ c_Recdef_Ocut ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ c_COMBS ) ) @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ ( D @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_fun ) @ ( D @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Recdef_Oadm__wf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adm__lemma) ).
thf(1325,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ c_COMBI @ ( B @ ( C @ ( D @ c_Recdef_Ocut ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ c_COMBS ) ) @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ ( D @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_fun ) @ ( D @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Recdef_Oadm__wf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [I: $i,J: $i,K: $i,L: $i] :
( ( B @ ( L @ ( K @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( J @ ( I @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( L @ ( K @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( L @ ( K @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( J @ ( I @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( E @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).
thf(1381,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [I: $i,J: $i,K: $i,L: $i] :
( ( B @ ( L @ ( K @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( J @ ( I @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( G @ ( H @ tc_prod ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( L @ ( K @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ ( G @ ( H @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( L @ ( K @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( J @ ( I @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) )
=> ( E @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
thf(2461,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ ( C @ ( F @ c_Fun_Ooverride__on ) ) ) ) ) )
= ( E @ ( B @ hAPP ) ) ) )
& ( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ ( C @ ( F @ c_Fun_Ooverride__on ) ) ) ) ) )
= ( E @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__def) ).
thf(1909,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ ( C @ ( F @ c_Fun_Ooverride__on ) ) ) ) ) )
= ( E @ ( B @ hAPP ) ) ) )
& ( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ ( C @ ( F @ c_Fun_Ooverride__on ) ) ) ) ) )
= ( E @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(496,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Recdef_Oadm__wf ) ) ) )
<=> ! [E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( B @ ( G @ ( H @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( H @ ( E @ hAPP ) )
= ( H @ ( F @ hAPP ) ) ) )
=> ( ( G @ ( E @ ( A @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( A @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adm__wf__def) ).
thf(2593,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( B @ ( G @ ( H @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( H @ ( E @ hAPP ) )
= ( H @ ( F @ hAPP ) ) ) )
=> ( ( G @ ( E @ ( A @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( A @ hAPP ) @ hAPP ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Recdef_Oadm__wf ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Recdef_Oadm__wf ) ) ) )
=> ! [E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( B @ ( G @ ( H @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( H @ ( E @ hAPP ) )
= ( H @ ( F @ hAPP ) ) ) )
=> ( ( G @ ( E @ ( A @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( A @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
thf(895,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( ~ ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( B @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
thf(1474,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( ( ( C @ ( B @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ~ ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( E @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) ) )
<=> ! [G: $i] :
( ( C @ ( B @ ( G @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( D @ hAPP ) )
= ( G @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cuts__eq) ).
thf(2401,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i] :
( ( C @ ( B @ ( G @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( D @ hAPP ) )
= ( G @ ( A @ hAPP ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( E @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( E @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) ) )
=> ! [G: $i] :
( ( C @ ( B @ ( G @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( D @ hAPP ) )
= ( G @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Relation_Osingle__valued ) ) )
=> ( ( D @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedD) ).
thf(2212,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Relation_Osingle__valued ) ) )
=> ( ( D @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(636,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__eq) ).
thf(1066,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(876,plain,
( ! [A: $i,B: $i] :
( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B != A ) )
& ! [A: $i,B: $i] :
( ( B != A )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(miniscope,[status(thm)],[875]) ).
thf(877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D != C )
| ~ ( D @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( D != C )
| ~ ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A ) ) ),
inference(cnf,[status(esa)],[876]) ).
thf(879,plain,
! [B: $i,A: $i] :
( ( B != A )
| ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(cnfConj,[status(thm)],[877]) ).
thf(882,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
| ( B != A ) ),
inference(lifteq,[status(thm)],[879]) ).
thf(883,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(simp,[status(thm)],[882]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(1015,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(185,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( B @ c_List_Olexord ) @ ( B @ tc_List_Olist @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__transI) ).
thf(1113,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
=> ( A @ ( B @ c_List_Olexord ) @ ( B @ tc_List_Olist @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_FunDef_Oin__rel ) ) ) ) )
<=> ( C @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rel__def) ).
thf(2633,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_FunDef_Oin__rel ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_FunDef_Oin__rel ) ) ) ) )
=> ( C @ ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( C @ ( F @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2I) ).
thf(2101,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( C @ ( F @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__same__eq) ).
thf(1364,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C = A )
=> ( ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Oequations_I2_J) ).
thf(1496,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
thf(1102,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
~ ( B @ ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( C @ c_List_Olexord ) @ ( A @ ( A @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__irreflexive) ).
thf(2156,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
~ ( B @ ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( C @ c_List_Olexord ) @ ( A @ ( A @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(653,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [G: $i,H: $i] :
( ( A
= ( H @ ( G @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( H @ ( G @ ( B @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitE) ).
thf(1198,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [G: $i,H: $i] :
( ( A
= ( H @ ( G @ ( C @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( H @ ( G @ ( B @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
thf(1396,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( F @ ( E @ ( A @ ( D @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( C @ ( E @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__cut__apply) ).
thf(1213,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( F @ ( E @ ( A @ ( D @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( C @ ( E @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(768,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(827,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(147,axiom,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistrelp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_Oequations_I1_J) ).
thf(986,plain,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistrelp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__dropWhile__id) ).
thf(2288,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(174,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(1076,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( E @ c_List_Olistrel ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( E @ c_List_Olistrel ) @ ( A @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( E @ c_List_Olistrel ) @ ( A @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__trans) ).
thf(1583,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( E @ c_List_Olistrel ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( E @ c_List_Olistrel ) @ ( A @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( E @ c_List_Olistrel ) @ ( A @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(531,plain,
( ~ ( sk2 @ ( v_P____ @ hAPP ) @ ( v_b____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( v_b____ @ ( v_c____ @ ( sk1 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(cnfConj,[status(thm)],[527]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le2) ).
thf(927,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( C @ ( A @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_below__Lin) ).
thf(1134,plain,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( C @ ( A @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__ident) ).
thf(1081,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olistrel1 ) @ ( A @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I1) ).
thf(1990,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olistrel1 ) @ ( A @ ( C @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
thf(1340,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(11,axiom,
tc_Nat_Onat @ class_Lattices_Osemilattice__inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
thf(553,plain,
tc_Nat_Onat @ class_Lattices_Osemilattice__inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(330,axiom,
! [A: $i] :
( ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ~ ~ ( A @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(1758,plain,
! [A: $i] :
( ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F = E )
=> ( ( F @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__weak__cong) ).
thf(2107,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F = E )
=> ( ( F @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
thf(1203,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(589,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
thf(795,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(50,axiom,
tc_Nat_Onat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(680,plain,
tc_Nat_Onat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(663,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( B @ ( c_fequal @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ c_Hilbert__Choice_OEps ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__def) ).
thf(2652,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= ( A @ ( B @ ( c_fequal @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ c_Hilbert__Choice_OEps ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(360,axiom,
~ ! [A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Odistinct ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(1905,plain,
~ ! [A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_ONil @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).
thf(1420,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(217,axiom,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistsp ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_ONil) ).
thf(1277,plain,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistsp ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olex ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) )
& ( A @ ( D @ c_List_Olexord ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__lex) ).
thf(2234,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) )
& ( A @ ( D @ c_List_Olexord ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ c_List_Olex ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_List_Olex ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) )
& ( A @ ( D @ c_List_Olexord ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2E) ).
thf(1748,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__acc__down) ).
thf(1516,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(160,axiom,
v_F @ c_Arrow__Order__Mirabelle_Ounanimity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_u) ).
thf(1025,plain,
v_F @ c_Arrow__Order__Mirabelle_Ounanimity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Odistinct ) )
=> ( B @ ( A @ c_List_Obutlast ) @ ( A @ c_List_Odistinct ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__butlast) ).
thf(872,plain,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( B @ ( A @ c_List_Odistinct ) )
=> ( B @ ( A @ c_List_Obutlast ) @ ( A @ c_List_Odistinct ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ ( D @ c_List_Olist_Olist__case ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).
thf(971,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( B @ ( C @ ( D @ c_List_Olist_Olist__case ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( F @ ( C @ c_List_Olistrelp ) ) ) )
=> ( A @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ ( C @ c_List_Olistrelp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_OCons) ).
thf(1566,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( F @ ( C @ c_List_Olistrelp ) ) ) )
=> ( A @ ( D @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ ( C @ c_List_Olistrelp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B
= ( C @ ( F @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ~ ( A @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ! [F: $i] :
( ( B
= ( F @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ~ ( A @ ( E @ c_List_Olistrel1 ) @ ( F @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__listrel1E1) ).
thf(1647,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B
= ( C @ ( F @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ~ ( A @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ! [F: $i] :
( ( B
= ( F @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ~ ( A @ ( E @ c_List_Olistrel1 ) @ ( F @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
thf(1780,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ c_List_Osplice ) ) )
= ( A @ ( C @ ( E @ c_List_Osplice ) ) @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I3_J) ).
thf(1484,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ c_List_Osplice ) ) )
= ( A @ ( C @ ( E @ c_List_Osplice ) ) @ ( B @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
thf(1098,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_Osingle__valued ) ) )
<=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__def) ).
thf(2689,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E = F ) ) )
=> ( A @ ( B @ ( C @ c_Relation_Osingle__valued ) ) ) )
& ( ( A @ ( B @ ( C @ c_Relation_Osingle__valued ) ) )
=> ! [D: $i,E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( A @ ( F @ ( D @ ( B @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E = F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__greatest) ).
thf(712,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OtakeWhile ) ) )
= ( B @ c_List_Olist_ONil ) ) )
& ( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OtakeWhile ) ) )
= ( A @ ( D @ ( B @ c_List_OtakeWhile ) ) @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).
thf(1770,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OtakeWhile ) ) )
= ( B @ c_List_Olist_ONil ) ) )
& ( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OtakeWhile ) ) )
= ( A @ ( D @ ( B @ c_List_OtakeWhile ) ) @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D2) ).
thf(1400,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Osplice ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice__Nil2) ).
thf(707,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Osplice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(515,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Oinsert ) ) )
= ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Nil) ).
thf(2732,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Oinsert ) ) )
= ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
thf(1252,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD1) ).
thf(1753,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(216,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Otrans ) )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__def) ).
thf(1267,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ c_Relation_Otrans ) ) )
& ( ( A @ ( B @ c_Relation_Otrans ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( A @ ( E @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( F @ ( G @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( F @ ( G @ tc_prod ) @ c_Set_Oimage ) ) ) @ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__imageI) ).
thf(2386,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( F @ ( G @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( F @ ( G @ tc_prod ) @ c_Set_Oimage ) ) ) @ ( D @ ( E @ ( A @ hAPP ) @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(519,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olistrel ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil1) ).
thf(2747,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olistrel ) @ ( B @ ( C @ c_List_Olist_ONil @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i,F: $i] :
( D
= ( F @ ( E @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( A @ ( C @ c_List_Olexord ) @ ( D @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__rightI) ).
thf(2569,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i,F: $i] :
( D
= ( F @ ( E @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) )
=> ( A @ ( C @ c_List_Olexord ) @ ( D @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(321,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ? [C: $i] :
( ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complete__Lin) ).
thf(1716,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ? [C: $i] :
( ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI1) ).
thf(791,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
thf(1188,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__assoc) ).
thf(1869,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(214,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olists ) @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists_ONil) ).
thf(1262,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_List_Olists ) @ ( B @ c_List_Olist_ONil @ ( B @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i] :
( C
!= ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self) ).
thf(1901,plain,
! [A: $i,B: $i,C: $i] :
( C
!= ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(509,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( F @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( G @ c_List_Olexord ) @ ( A @ ( E @ ( G @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( G @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( G @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( G @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( G @ tc_List_Olist @ ( G @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ tc_List_Olist @ ( G @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__left__rightI) ).
thf(2701,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( F @ ( G @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( G @ c_List_Olexord ) @ ( A @ ( E @ ( G @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( G @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( F @ ( G @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( G @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( G @ tc_List_Olist @ ( G @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ tc_List_Olist @ ( G @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(2275,plain,
v_a____ != v_b____,
inference(polarity_switch,[status(thm)],[2274]) ).
thf(2276,plain,
v_b____ != v_a____,
inference(lifteq,[status(thm)],[2275]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL )
<=> ! [D: $i,E: $i] : ( E @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(2219,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] : ( E @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
=> ! [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ! [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] : ( E @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(543,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(544,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ~ ( C @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[543]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_List_Olists ) @ ( B @ ( C @ c_List_Olists ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__mono) ).
thf(907,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_List_Olists ) @ ( B @ ( C @ c_List_Olists ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( B @ ( C @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( D @ c_FuncSet_Orestrict ) ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__restrict) ).
thf(1543,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( B @ ( C @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( D @ c_FuncSet_Orestrict ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_List_Olistsp ) @ ( B @ ( C @ c_List_Olistsp ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__mono) ).
thf(1023,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_List_Olistsp ) @ ( B @ ( C @ c_List_Olistsp ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) )
= ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__image) ).
thf(1702,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( C @ c_Set_Oimage ) ) ) @ ( D @ ( E @ ( F @ c_Set_Oimage ) ) ) )
= ( A @ ( B @ ( D @ ( C @ ( E @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( E @ ( C @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(613,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A = B )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( C @ c_Transitive__Closure_Ortrancl ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
thf(2543,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( C @ c_Transitive__Closure_Ortrancl ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__conv) ).
thf(1284,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityI) ).
thf(864,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( C @ ( E @ ( F @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( E = F )
| ( C @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( C @ ( D @ c_List_Olexord ) @ ( B @ ( A @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( C @ ( D @ c_List_Olexord ) @ ( A @ ( B @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__linear) ).
thf(2722,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( C @ ( E @ ( F @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( E = F )
| ( C @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( C @ ( D @ c_List_Olexord ) @ ( B @ ( A @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( C @ ( D @ c_List_Olexord ) @ ( A @ ( B @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_COMBI @ ( E @ ( E @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( B @ ( D @ ( E @ ( E @ c_FuncSet_Ocompose ) ) ) ) ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__Id) ).
thf(1881,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_COMBI @ ( E @ ( E @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( B @ ( D @ ( E @ ( E @ c_FuncSet_Ocompose ) ) ) ) ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI2) ).
thf(859,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__some) ).
thf(1972,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
thf(1052,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( D @ ( B @ ( C @ ( E @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__in__funcset) ).
thf(1506,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( D @ ( B @ ( C @ ( E @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(294,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(1585,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infE) ).
thf(1094,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Relation_OId__on ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__iff) ).
thf(2511,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C = B ) )
=> ( A @ ( D @ c_Relation_OId__on ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_Relation_OId__on ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( G @ ( H @ tc_prod ) @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( F @ ( G @ ( H @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( F @ ( C @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__twice) ).
thf(1372,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( A @ ( B @ ( G @ ( H @ tc_prod ) @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( C @ ( F @ ( G @ ( H @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( F @ ( C @ tc_fun ) @ ( G @ ( H @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(595,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(627,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( D @ c_Relation_Osingle__valued ) ) )
=> ( B @ ( C @ ( D @ c_Relation_Osingle__valued ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__subset) ).
thf(2045,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( D @ c_Relation_Osingle__valued ) ) )
=> ( B @ ( C @ ( D @ c_Relation_Osingle__valued ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
<=> ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__append__conv2) ).
thf(1180,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A
= ( B @ c_List_Olist_ONil ) )
=> ( C
= ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) )
& ( ( C
= ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( A
= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
thf(581,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_List_Olistrel ) @ ( A @ ( B @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( F @ c_List_Olistrel ) @ ( A @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel_OCons) ).
thf(2215,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_List_Olistrel ) @ ( A @ ( B @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( F @ c_List_Olistrel ) @ ( A @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(72,axiom,
tc_HOL_Obool @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(759,plain,
tc_HOL_Obool @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ ( C @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( D @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__below) ).
thf(1216,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( D @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) )
=> ( D @ ( E @ ( C @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( E @ ( C @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( A @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( D @ ( B @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ ( G @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitD_H) ).
thf(1575,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( F @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ ( G @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OdropWhile ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OdropWhile ) ) )
= ( A @ ( D @ ( B @ c_List_OdropWhile ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).
thf(2658,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OdropWhile ) ) )
= ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ) )
& ( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ ( B @ c_List_OdropWhile ) ) )
= ( A @ ( D @ ( B @ c_List_OdropWhile ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI1) ).
thf(771,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil )
!= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).
thf(1316,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil )
!= ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orotate1 ) @ ( B @ c_List_Odistinct ) )
<=> ( A @ ( B @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct1__rotate) ).
thf(1084,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Odistinct ) )
=> ( A @ ( B @ c_List_Orotate1 ) @ ( B @ c_List_Odistinct ) ) )
& ( ( A @ ( B @ c_List_Orotate1 ) @ ( B @ c_List_Odistinct ) )
=> ( A @ ( B @ c_List_Odistinct ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct ) )
=> ( B @ ( A @ ( C @ c_List_Oinsert ) ) @ ( C @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__insert) ).
thf(931,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct ) )
=> ( B @ ( A @ ( C @ c_List_Oinsert ) ) @ ( C @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i,F: $i] :
( ( A @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i,H: $i] :
( ( C
= ( H @ ( E @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( G @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( B
!= ( H @ ( F @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( G @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1E) ).
thf(1157,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel1 ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i,F: $i] :
( ( A @ ( F @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i,H: $i] :
( ( C
= ( H @ ( E @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( G @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( B
!= ( H @ ( F @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( G @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Osimps) ).
thf(1834,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( F @ c_List_Olistrel1 ) @ ( F @ c_List_Olist_ONil @ ( B @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ c_List_Olist_ONil @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( B @ ( D @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( D = B )
& ( A @ ( F @ c_List_Olistrel1 ) @ ( C @ ( E @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).
thf(2310,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ( A @ ( B @ ( D @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( D = B )
& ( A @ ( F @ c_List_Olistrel1 ) @ ( C @ ( E @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( F @ c_List_Olistrel1 ) @ ( F @ c_List_Olist_ONil @ ( B @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ c_List_Olist_ONil @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( F @ c_List_Olistrel1 ) @ ( F @ c_List_Olist_ONil @ ( B @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ c_List_Olist_ONil @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( D @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = C ) )
| ( ( D = B )
& ( A @ ( F @ c_List_Olistrel1 ) @ ( C @ ( E @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( D @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
thf(1844,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( D @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C = A )
=> ( B @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orotate1 ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__rotate1) ).
thf(688,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Orotate1 ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_ORangeP ) ) ) )
<=> ( B @ ( C @ ( D @ c_Relation_ORange ) ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).
thf(2707,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Relation_ORange ) ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_ORangeP ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Predicate_ORangeP ) ) ) )
=> ( B @ ( C @ ( D @ c_Relation_ORange ) ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(414,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL )
<=> ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__ex) ).
thf(2167,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL )
=> ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( B @ c_Relation_ORange ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
~ ( A @ ( C @ ( E @ ( D @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeE) ).
thf(2135,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( B @ c_Relation_ORange ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
~ ( A @ ( C @ ( E @ ( D @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(482,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( F
= ( H @ ( G @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ( H @ ( G @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( F @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitI2) ).
thf(2532,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i,H: $i] :
( ( F
= ( H @ ( G @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ( H @ ( G @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( F @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( D @ ( E @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
thf(946,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(1852,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
inference(cnf,[status(esa)],[1851]) ).
thf(1853,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
inference(lifteq,[status(thm)],[1852]) ).
thf(1854,plain,
! [A: $i] : ( A @ ( A @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
inference(simp,[status(thm)],[1853]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ c_List_Olists ) @ ( A @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__lists__eq) ).
thf(2526,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_List_Olists ) @ ( A @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_List_Olists ) @ ( A @ ( C @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(961,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).
thf(813,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Osemilattice__inf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
thf(995,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Osemilattice__inf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcsetI) ).
thf(2152,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetD) ).
thf(1689,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(568,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(123,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Id__on) ).
thf(914,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(129,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ ( B @ c_Relation_Osingle__valued ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
thf(929,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ ( B @ c_Relation_Osingle__valued ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitI) ).
thf(2162,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( G @ tc_fun ) @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(684,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
thf(549,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(1994,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__inf__iff) ).
thf(716,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(458,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__caseI) ).
thf(2399,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( tc_HOL_Obool @ ( A @ ( B @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
thf(2041,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_Ocurry ) ) ) @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__curry) ).
thf(1308,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_Ocurry ) ) ) @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__def) ).
thf(2198,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryE) ).
thf(2019,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ ( E @ c_Product__Type_Ocurry ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_Wellfounded_Oacc ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downward) ).
thf(1642,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_Wellfounded_Oacc ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__leq) ).
thf(2302,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( E @ hAPP ) @ ( D @ ( E @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ ( B @ c_Wellfounded_Omlex__prod ) ) @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( A @ ( B @ c_List_Olast ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__appendL) ).
thf(1280,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( A @ ( B @ c_List_Olast ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Wellfounded_Oacc ) @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
thf(1678,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Wellfounded_Oacc ) @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olexord ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olexord ) @ ( C @ ( A @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__leftI) ).
thf(2255,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_List_Olexord ) @ ( C @ ( D @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_List_Olexord ) @ ( C @ ( A @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Cons) ).
thf(1546,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).
thf(818,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(351,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil) ).
thf(1876,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( E @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( D @ ( B @ hAPP ) )
= ( C @ ( B @ hAPP ) ) ) )
| ( C @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measures_I2_J) ).
thf(2008,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( A @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( D @ ( B @ hAPP ) )
= ( C @ ( B @ hAPP ) ) ) )
| ( C @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ ( E @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ ( E @ tc_fun ) @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( E @ c_List_Omeasures ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( D @ ( B @ hAPP ) )
= ( C @ ( B @ hAPP ) ) ) )
| ( C @ ( B @ hAPP ) @ ( D @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(195,axiom,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil2) ).
thf(1148,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Oappend @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
thf(867,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntI) ).
thf(1480,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(26,axiom,
tc_HOL_Obool @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(603,plain,
tc_HOL_Obool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
thf(999,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(620,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
thf(1578,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(4347,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
!= ( B @ hBOOL ) )
| ~ $true
| ~ ( B @ ( c_fNot @ hAPP ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[1854,2568]) ).
thf(4348,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
!= ( B @ hBOOL ) )
| ~ ( B @ ( c_fNot @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[4347]) ).
thf(4349,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_fequal @ hAPP ) @ hAPP ) @ ( c_fNot @ hAPP ) @ hBOOL ),
inference(pattern_uni,[status(thm)],[4348:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( c_fequal @ hAPP ) @ hAPP ) ))]]) ).
thf(4399,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_fequal @ hAPP ) @ hAPP ) @ ( c_fNot @ hAPP ) @ hBOOL ),
inference(simp,[status(thm)],[4349]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct ) )
=> ( B @ ( A @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Odistinct ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__dropWhile) ).
thf(950,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_List_Odistinct ) )
=> ( B @ ( A @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Odistinct ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(494,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Olast ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__snoc) ).
thf(2587,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_List_Olist_ONil @ ( A @ ( C @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ c_List_Olast ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(13,axiom,
tc_Nat_Onat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(564,plain,
tc_Nat_Onat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).
thf(2334,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_List_Olistrel1 ) @ ( D @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(897,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( C = B )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olexord ) @ ( B @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
~ ( A @ ( F @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ c_List_Olexord ) @ ( B @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__leftD) ).
thf(2091,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ c_List_Olexord ) @ ( B @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
~ ( A @ ( F @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( E @ c_List_Olexord ) @ ( B @ ( C @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ tc_List_Olist @ ( E @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(532,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_List_Orotate1 ) )
= ( B @ c_List_Olist_ONil ) )
<=> ( A
= ( B @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__is__Nil__conv) ).
thf(696,plain,
! [A: $i,B: $i] :
( ( ( A
= ( B @ c_List_Olist_ONil ) )
=> ( ( A @ ( B @ c_List_Orotate1 ) )
= ( B @ c_List_Olist_ONil ) ) )
& ( ( ( A @ ( B @ c_List_Orotate1 ) )
= ( B @ c_List_Olist_ONil ) )
=> ( A
= ( B @ c_List_Olist_ONil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_Osimps) ).
thf(1165,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( B @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le1) ).
thf(955,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__inf) ).
thf(886,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) )
= ( D @ c_HOL_Oundefined ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__arb) ).
thf(2201,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) )
= ( D @ c_HOL_Oundefined ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greatest) ).
thf(918,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD2) ).
thf(2021,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last_Osimps) ).
thf(1346,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
!= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= ( C @ ( B @ c_List_Olast ) ) ) )
& ( ( C
= ( B @ c_List_Olist_ONil ) )
=> ( ( C @ ( A @ ( B @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ c_List_Olast ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__assoc) ).
thf(624,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate2D) ).
thf(2159,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(463,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( D @ ( B @ ( C @ ( E @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrictI) ).
thf(2430,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( D @ ( B @ ( C @ ( E @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( E @ ( B @ hAPP ) ) )
=> ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
thf(2485,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( E @ ( B @ hAPP ) ) )
=> ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) ) @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( E @ ( F @ ( G @ ( H @ c_Set_Oimage ) ) ) )
= D )
=> ( ( ( D @ ( B @ ( C @ ( G @ c_Set_Oimage ) ) ) )
= A )
=> ( ( E @ ( F @ ( B @ ( E @ ( C @ ( G @ ( H @ c_FuncSet_Ocompose ) ) ) ) ) @ ( C @ ( H @ c_Set_Oimage ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__compose) ).
thf(1019,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( E @ ( F @ ( G @ ( H @ c_Set_Oimage ) ) ) )
= D )
=> ( ( ( D @ ( B @ ( C @ ( G @ c_Set_Oimage ) ) ) )
= A )
=> ( ( E @ ( F @ ( B @ ( E @ ( C @ ( G @ ( H @ c_FuncSet_Ocompose ) ) ) ) ) @ ( C @ ( H @ c_Set_Oimage ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(644,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__in__listsp__conv) ).
thf(1357,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) @ ( B @ ( B @ c_Relation_ORange ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Id__on) ).
thf(992,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_OId__on ) @ ( B @ ( B @ c_Relation_ORange ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( F @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_List_Olistrel1 ) @ ( F @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( F @ c_List_Olistrel1 ) @ ( F @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).
thf(1923,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( F @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( F @ c_List_Olistrel1 ) @ ( F @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( F @ c_List_Olistrel1 ) @ ( F @ tc_List_Olist @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_prod ) @ c_Hilbert__Choice_OEps ) )
= ( B @ ( C @ c_Product__Type_OPair ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ ( C @ tc_prod ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_Hilbert__Choice_OEps ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__Eps) ).
thf(1925,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ tc_prod ) @ c_Hilbert__Choice_OEps ) )
= ( B @ ( C @ c_Product__Type_OPair ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( B @ ( C @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ ( C @ tc_prod ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( C @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( B @ ( C @ tc_prod ) @ c_Hilbert__Choice_OEps ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb2) ).
thf(850,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( B @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__mono) ).
thf(1597,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( B @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(54,axiom,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistrelp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_ONil) ).
thf(691,plain,
! [A: $i,B: $i] : ( B @ c_List_Olist_ONil @ ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Olistrelp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Hilbert__Choice_OEps ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__trivial) ).
thf(1120,plain,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Hilbert__Choice_OEps ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(607,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(406,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( C @ ( F @ c_List_Olistrel1 ) @ ( A @ ( B @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = D ) )
| ( ( B = A )
& ( C @ ( F @ c_List_Olistrel1 ) @ ( D @ ( E @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( C @ ( F @ c_List_Olistrel1 ) @ ( A @ ( D @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__listrel1I) ).
thf(2138,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( C @ ( F @ c_List_Olistrel1 ) @ ( A @ ( B @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( E = D ) )
| ( ( B = A )
& ( C @ ( F @ c_List_Olistrel1 ) @ ( D @ ( E @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( C @ ( F @ c_List_Olistrel1 ) @ ( A @ ( D @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ tc_List_Olist @ ( F @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
thf(1331,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__infI) ).
thf(2754,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(1320,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__commute) ).
thf(659,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) )
= C )
=> ( ( B
= ( A @ ( D @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__appendI) ).
thf(1416,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) )
= C )
=> ( ( B
= ( A @ ( D @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) )
=> ( ( B @ ( E @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( F @ c_List_Oappend @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olistrel ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( C @ c_List_Olist_ONil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil2) ).
thf(1917,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_List_Olistrel ) @ ( C @ c_List_Olist_ONil @ ( B @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B
= ( C @ c_List_Olist_ONil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__conv) ).
thf(2453,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(397,axiom,
c_Arrow__Order__Mirabelle_OProf @ ( v_P_H____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096P_H_A_058_AProf_096) ).
thf(2106,plain,
c_Arrow__Order__Mirabelle_OProf @ ( v_P_H____ @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(503,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( A @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ ( A @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_List_Obutlast ) @ ( A @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__butlast__last__id) ).
thf(2655,plain,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_List_Olist_ONil ) )
=> ( ( A @ c_List_Olist_ONil @ ( B @ ( A @ c_List_Olast ) @ ( A @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_List_Obutlast ) @ ( A @ c_List_Oappend @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev__mp) ).
thf(1945,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI) ).
thf(1009,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(923,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oord )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).
thf(1737,plain,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C2_C) ).
thf(2438,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(1037,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__dropWhile__le) ).
thf(775,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(24637,plain,
$false,
inference(e,[status(thm)],[892,2094,1469,2744,1633,1105,2412,909,2499,777,1818,1549,2280,1686,1879,1337,760,2341,2336,2031,2427,1982,1855,762,1406,1443,2590,1422,741,1205,2114,1437,861,1173,2099,1591,655,2380,1137,1327,1260,2459,2146,1458,2195,1705,1164,797,2434,1872,670,2575,1746,1782,841,1046,1482,651,2173,565,1628,724,1287,570,1792,2735,785,1323,2274,2185,2562,1832,1992,949,1760,1298,1264,2217,1313,1279,542,2703,1379,1514,2552,1890,969,1013,1398,1115,1815,1778,2388,1100,2713,638,853,1931,1568,2520,2730,2456,1302,789,591,646,834,1151,2291,821,905,1714,2027,1040,2893,2469,1858,2122,4660,1377,634,734,1886,2523,1622,1394,1526,2809,1433,1104,1521,2508,981,2367,1928,988,2639,2103,2750,920,942,2204,1153,810,2047,1311,2641,2083,714,1636,1057,529,1691,546,793,2364,2164,1387,957,746,952,1123,1487,693,2606,1824,2277,1355,1580,1676,2133,916,1938,1032,1920,2477,2565,2332,1178,1888,583,2181,1656,1079,2741,1740,551,1128,1392,2228,1291,710,1573,974,1983,1851,2377,1375,2509,2537,869,1755,1118,2300,578,1534,2685,1540,1006,1659,933,554,1461,1424,1842,1937,2666,1644,706,1028,2023,901,2419,997,2304,1131,1974,2243,2581,721,1947,1874,1599,2756,622,837,2125,1588,984,911,2505,1333,938,805,1035,1026,662,2546,2761,765,1712,1054,530,2617,773,586,2338,1680,1698,2149,824,856,573,1727,1510,904,1389,2489,2568,743,2806,1403,1520,545,2225,1884,843,1125,875,577,711,641,1503,2193,936,1707,1865,2759,1090,704,1638,540,2029,2326,611,787,1897,804,2573,2358,604,1194,831,681,2383,1011,1524,2097,2257,2246,2116,1571,1175,1048,736,1722,2669,649,1043,1471,2025,631,758,2343,816,2111,848,1325,1381,2461,799,1909,2593,895,1474,2401,2212,636,1066,883,1015,1113,2633,2101,1364,1496,1102,2156,653,1198,1396,1213,768,827,986,2288,1076,1583,531,927,1134,1081,1990,1340,553,1758,2107,1203,589,795,680,663,2652,1905,1420,1277,2234,2567,1748,525,1516,1025,872,971,1566,1647,1780,1484,1098,2689,712,1770,1400,707,2732,1252,1753,1267,2386,2747,2569,1716,791,1188,1869,1262,1901,2701,2276,2219,544,907,1543,1023,1702,613,2543,1284,864,2722,1881,859,1972,1052,1506,1585,1094,2511,1372,595,627,2045,1180,581,2215,759,1216,1575,2658,771,1316,1084,931,539,1157,1834,2310,1844,688,903,2707,2167,2135,2532,946,1854,2526,961,813,995,2152,1689,568,914,929,2162,684,549,2917,1994,716,2399,2041,1308,2198,2779,536,2019,1642,2302,1280,1678,2255,1546,818,1876,2008,1148,867,1480,603,999,620,1578,4399,950,2587,564,2334,897,2091,532,696,1165,955,886,2201,918,2021,1346,624,2159,2430,2485,1019,528,644,1357,992,1923,1925,850,1597,691,1120,607,2138,1331,2754,1320,659,543,1416,1917,2453,2106,2655,1945,1009,923,1737,2438,1037,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT139+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.38 % Computer : n014.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 06:32:16 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.41/1.40 % [INFO] Parsing done (447ms).
% 2.41/1.42 % [INFO] Running in sequential loop mode.
% 3.32/1.81 % [INFO] eprover registered as external prover.
% 3.32/1.82 % [INFO] Scanning for conjecture ...
% 4.10/2.05 % [INFO] Found a conjecture (or negated_conjecture) and 522 axioms. Running axiom selection ...
% 5.32/2.35 % [INFO] Axiom selection finished. Selected 522 axioms (removed 0 axioms).
% 6.88/2.87 % [INFO] Problem is first-order (TPTP FOF).
% 7.13/2.91 % [INFO] Type checking passed.
% 7.13/2.92 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 89.82/23.47 % External prover 'e' found a proof!
% 89.82/23.47 % [INFO] Killing All external provers ...
% 89.82/23.47 % Time passed: 22946ms (effective reasoning time: 22042ms)
% 89.82/23.47 % 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)>
% 89.82/23.48 % Axioms used in derivation (522): fact_order__le__neq__trans, fact_transI, fact_xt1_I1_J, fact_converse__rtrancl__induct2, arity_fun__Orderings_Oorder, fact_Int__lower1, fact_dropWhile_Osimps_I2_J, fact_adm__wf__def, fact_Pi__I, fact_single__valued__Id__on, fact_append__Nil2, fact_cut__apply, fact_le__inf__iff, fact_accp_Oequations, fact_inf2I, fact_lexord__append__leftI, fact_order__le__less__trans, fact_lexord__lex, fact__C1_C, fact_last__appendR, arity_Nat__Onat__Lattices_Olattice, fact_IIA__def, fact_funcset__image, fact_termination__basic__simps_I5_J, fact_cut__def, fact_unanimity__def, fact_compose__Id, fact_Range__Int__subset, fact_inf__sup__aci_I4_J, fact_inf_Oassoc, fact_listrel1E, fact_inv__into__into, fact_nat__less__cases, fact_Pi__mono, fact_xt1_I4_J, fact_listrel__Cons1, fact_Cons__listrel1E2, fact_restrictI, fact_curry__split, fact_lists__IntI, fact_prod_Orecs, fact_length__rotate1, fact_self__append__conv, fact_linorder__not__le, fact_curry__conv, fact_lexn__length, fact_order__less__asym_H, fact_third__alt, arity_Nat__Onat__Orderings_Oorder, fact_curry__def, fact_order__eq__refl, fact_Pi__I_H, fact_Id__compose, fact_in__mktop, fact_inf__absorb1, fact_extensionalityI, fact_in__mkbot, fact_linorder__neqE, fact_curryE, fact_leI, fact_Int__left__commute, fact_assms_I1_J, fact_trans__Id__on, arity_fun__Lattices_Olattice, fact_rtrancl_Ortrancl__refl, fact_Pi__anti__mono, fact_linorder__antisym__conv2, fact_acc_Osimps, arity_Nat__Onat__Lattices_Osemilattice__inf, fact_measures__lesseq, arity_HOL__Obool__Orderings_Opreorder, fact_listrel__subset__rtrancl__listrel1, fact_listrelp_Oequations_I2_J, help_c__fconj__3, fact_image__Int__subset, fact_Cons__acc__listrel1I, fact_below__Lin, fact_pred__equals__eq2, fact_rtrancl__listrel1__if__listrel, fact_dropWhile__eq__Cons__conv, fact_inf__sup__ord_I2_J, help_c__fequal__2, fact_linorder__antisym__conv3, fact_order__less__imp__not__eq, fact_rtrancl__mono, fact_rtrancl__subset__rtrancl, fact_listsp_Oequations_I2_J, help_c__COMBC__1, fact_prod_Osimps_I2_J, fact_split__paired__All, fact_append__is__Nil__conv, fact_complete__Lin, fact_list_Osimps_I3_J, fact_Cons__in__lists__iff, fact_lists_ONil, fact_inf__fun__def, fact_acc_OaccI, fact_measures__less, fact_converse__rtranclE2, fact_image__image, fact_extensional__funcset__def, fact_less__infI2, fact_linorder__antisym__conv1, fact_inf1D2, fact_splice_Osimps_I3_J, fact_equalityD2, fact_append1__eq__conv, fact_inf_Oleft__commute, fact_predicate2D, fact_listrel_ONil, fact_le__funD, fact_lists__accI, fact_Pi__mem, fact_inf2D1, fact_splice_Osimps_I2_J, fact_listrel_OCons, fact_le__fun__def, fact_acc__subset, fact_extensional__funcset__mem, fact_neq__if__length__neq, help_c__COMBS__1, fact_split__twice, fact_override__on__def, fact_Eps__split__eq, arity_fun__Lattices_Osemilattice__inf, fact_ord__less__eq__trans, fact_in__mono, fact_trans__Int, fact_Int__absorb2, fact_xt1_I9_J, help_c__COMBI__1, fact_linorder__less__linear, fact_order__less__imp__not__less, fact_takeWhile__dropWhile__id, fact_rotate__simps, fact_lists__mono, fact_lexord__transI, fact_inf__Int__eq, fact_someI__ex, fact_extensional__funcset__arb, fact_mem__splitE, fact_Int__assoc, fact_list_Osimps_I2_J, fact_in__measure, fact_listrelp__listrel__eq, fact_rtrancl__subset, fact_image__restrict__eq, fact_subset__iff__psubset__eq, fact_single__valued__subset, fact_Id__on__iff, fact_mkbot__Lin, fact_mem__splitI, fact_less__or__eq__imp__le, fact_rtrancl__listrel1__ConsI1, arity_HOL__Obool__Lattices_Olattice, fact_funcset__mem, fact_rev__image__eqI, fact_distinct__takeWhile, fact_tfl__cut__apply, fact_inv__into__def, fact_append__listrel1I, help_c__fconj__2, fact_listsp_ONil, fact_lexord__append__left__rightI, arity_Nat__Onat__Orderings_Opreorder, fact_listrel__trans, fact_last__appendL, fact_inf__commute, fact_order__antisym, fact_xt1_I10_J, fact_less__irrefl__nat, fact_length__takeWhile__le, fact_order__less__imp__not__eq2, fact_takeWhile__tail, fact_order__refl, fact_append__self__conv2, fact_acc__downwards, fact_dictator__def, fact_inf1I, fact_inf_Oidem, fact_Domain__mono, fact_xt1_I5_J, help_c__fNot__1, fact_butlast__snoc, fact_inf2E, fact_listsp__infI, fact_maps__simps_I2_J, fact_listrel__rtrancl__refl, fact_adm__lemma, fact_RangeI, fact_Nil__notin__lex, fact_le__infI2, fact_nat__neq__iff, fact_compose__extensional, fact_DomainI, fact__C2_C, fact_inf__sup__ord_I1_J, fact_inf1E, fact_Pi__cong, fact_inf__left__commute, fact_distinct_Osimps_I1_J, fact_append__self__conv, fact_inf__left__idem, fact_xt1_I3_J, fact_less__imp__neq, fact_xt1_I8_J, fact_listsp__conj__eq, fact_predicate1D, fact_less__not__refl3, fact_eq__mem, fact_append__in__lists__conv, fact_butlast_Osimps_I2_J, fact_notin__Lin__iff, fact_accp__subset, fact_some__eq__ex, arity_HOL__Obool__Orderings_Oord, fact__096a_A_126_061_Ab_096, fact_Id__onE, fact_RangeE, fact_compose__assoc, fact_dropWhile_Osimps_I1_J, fact_less__infI1, fact_list_Oinject, fact__096P_H_A_058_AProf_096, fact_eqset__imp__iff, fact_order__neq__le__trans, fact_splitI, fact_equalityD1, fact_converse__rtrancl__into__rtrancl, fact_pair__imageI, fact_inf2D2, fact_extensional__arb, fact_append__butlast__last__id, fact_same__fstI, fact_subset__image__iff, fact_trans__def, fact_le__funE, fact_rotate1__def, arity_Nat__Onat__Orderings_Oord, fact_lexord__Nil__right, arity_fun__Orderings_Opreorder, fact_rtrancl__trans, fact_irrefl__def, fact_Int__lower2, fact_override__on__apply__in, fact_extensional__restrict, help_c__fequal__1, fact_in__above, fact_linorder__neq__iff, fact_DomainP__Domain__eq, fact_in__below, fact_Int__absorb, fact_ord__le__eq__trans, fact_le__infE, fact_not__Cons__self, fact_mlex__leq, fact_listrel__Cons2, fact_set__mp, fact_listsp__lists__eq, fact_DomainP_Ointros, fact_funcset__compose, fact_accp__downward, fact_not__less__iff__gr__or__eq, fact_mktop__Lin, fact_listrel__Nil1, fact_Id__on__def_H, fact_listrel__reflcl__if__listrel1, fact_append__same__eq, fact_Range__Id__on, fact_lists__accD, fact_linorder__neqE__nat, fact_psubsetD, fact_le__iff__inf, fact_listrel1__eq__len, fact_distinct__butlast, fact_compose__id__inv__into, fact_set__eq__subset, fact_listsp_Osimps, fact_surj__compose, fact_pred__subset__eq, fact_inf_Ocommute, fact_eq__Nil__appendI, fact_iff, fact_order__less__le, fact_inf__greatest, fact_Range__iff, help_c__fconj__1, fact_Nitpick_Orefl_H__def, fact_append__Nil, fact_inv__into__injective, fact_Pair__inject, fact_xt1_I12_J, fact_subset__refl, fact_inf__le1, fact_inf1D1, fact_listsp__mono, fact_last__append, fact_RangeP_Ointros, fact_snoc__eq__iff__butlast, fact_inf__Int__eq2, fact_last_Osimps, fact_lexord__cons__cons, arity_fun__Orderings_Oord, fact_equalityI, fact_ext, fact_order__less__not__sym, fact_split__paired__Eps, help_c__fNot__2, arity_HOL__Obool__Orderings_Oorder, fact_linorder__le__less__linear, fact_snoc__listrel1__snoc__iff, fact_internal__split__conv, fact_single__valued__confluent, fact_le__infI, fact_append__Cons, fact_Cons__in__lex, fact_someI, fact_Int__commute, fact_less__le__not__le, arity_Nat__Onat__Orderings_Olinorder, fact_compose__def, fact_mem__splitI2, fact_linorder__le__cases, fact_inf__apply, fact_assms_I3_J, fact_Id__on__eqI, fact_inf__mono, fact_in__measures_I2_J, fact_listrel1I2, fact_order__less__le__trans, fact_prod__caseI, fact_Nil2__notin__lex, fact_RangeP__Range__eq, fact_PiE, fact_rtrancl__induct2, fact_split__eta, fact_insert__Nil, help_c__COMBB__1, fact_listrel__eq__len, fact_not__leE, fact_leD, fact_lexord__append__leftD, fact_internal__split__def, fact__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096, fact_listrel1I, fact_override__on__apply__notin, fact_distinct__insert, fact_IntD2, fact_extensional__subset, fact_order__less__asym, fact_curryD, fact_lexord__Nil__left, fact_mlex__less, fact_psubset__imp__subset, fact_set__rev__mp, fact_Domain__iff, fact_inf__absorb2, fact_eq__mem__trans, fact_Int__mono, fact_trans__lex__prod, fact_last__snoc, fact_acc__downwards__aux, fact_list_Osimps_I5_J, fact_not__Cons__self2, fact_inv__into__funcset, fact_maps__simps_I1_J, fact_RangeP_Oequations, fact_rotate1__is__Nil__conv, fact_funcset__id, arity_HOL__Obool__Lattices_Osemilattice__inf, fact_rev__predicate2D, fact_transD, fact_single__valuedI, fact_less__not__refl2, fact_single__valued__def, fact_distinct__dropWhile, fact_takeWhile_Osimps_I1_J, fact_linorder__linear, fact__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_append__eq__appendI, fact_DomainE, fact_xt1_I6_J, fact_Domain__Int__subset, fact_accp_Osimps, fact_distinct1__rotate, fact_listrel__mono, fact_linorder__not__less, fact_append__assoc, fact_in__lex__prod, fact_image__inv__into__cancel, fact_restrict__apply, fact_inf__sup__aci_I3_J, fact_last__ConsL, fact_in__measures_I1_J, fact_listrel__Nil2, fact_listrelp_Oequations_I1_J, fact_tfl__some, fact_append__eq__Cons__conv, fact_Int__absorb1, fact_listsp__inf__eq, fact_less__fun__def, fact_rev__predicate1D, fact_listrel__rtrancl__eq__rtrancl__listrel1, fact_trans__rtrancl, fact_Domain__Id__on, fact_cuts__eq, fact_inf_Oleft__idem, fact__096P_A_058_AProf_096, fact_xt1_I2_J, fact_rtrancl__listrel1__eq__len, fact_in__rel__def, fact_split__conv, fact_subset__psubset__trans, fact_listrelp_OCons, fact_accp__acc__eq, fact_splitD, fact_split__weak__cong, fact_order__eq__iff, fact_equalityE, fact_split__curry, fact_Pair__eq, fact_restrict__in__funcset, fact_image__iff, fact_inf__assoc, fact_rtrancl_Ortrancl__into__rtrancl, fact_Lin__irrefl, fact_listrel1I1, fact_ord__eq__less__trans, fact_append__in__listsp__conv, fact_inf__le2, help_c__COMBK__1, fact_equalityCE, fact_r__into__rtrancl, fact_dist, fact_restrict__def, fact_Not__Domain__rtrancl, fact_image__eqI, fact_subsetD, fact_Cons__eq__append__conv, fact_above__Lin, fact_psubset__eq, fact_funcsetI, fact_u, fact_rtrancl__idemp, fact_Cons__listrel1E1, fact_not__Nil__listrel1, fact_IntI, fact_listrel1__mono, fact_splice__Nil2, fact_partition_Osimps_I2_J, fact_image__ident, fact_partition_Osimps_I1_J, fact_some__eq__trivial, fact_lexord__linear, fact_impossible__Cons, fact_image__mono, fact_Cons__eq__appendI, fact_not__listrel1__Nil, fact_order__le__imp__less__or__eq, fact_list_Osimps_I4_J, fact_some__sym__eq__trivial, fact_acc__downward, fact_butlast__append, fact_takeWhile_Osimps_I2_J, fact_dictatorI, fact_Nil__is__append__conv, fact_append__eq__append__conv2, fact_listrel__rtrancl__trans, fact_curryI, fact_splice_Osimps_I1_J, fact_order__antisym__conv, fact_f__inv__into__f, fact_last__ConsR, fact_rev__induct, fact_eqelem__imp__iff, fact_pred__equals__eq, fact_listsp_Oequations_I1_J, fact_Int__greatest, fact_psubset__subset__trans, fact_subset__trans, fact_IntE, fact_inf__sup__aci_I2_J, fact_rtrancl__listrel1__ConsI2, fact_order__less__trans, fact_le__infI1, fact_IntD1, fact__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_058_AProf_096, fact_compose__eq, fact_order__less__irrefl, fact_Int__iff, fact_listrel1__rtrancl__subset__rtrancl__listrel1, fact_order__le__less, fact_Int__left__absorb, fact_order__less__imp__le, fact_mem__def, fact_length__dropWhile__le, fact_inf__sup__aci_I1_J, fact_lists__Int__eq, fact_Cons__listrel1__Cons, fact_ord__eq__le__trans, fact_takeWhile__not__last, fact_pred__subset__eq2, fact_inf__idem, fact_linorder__cases, fact_xt1_I11_J, fact_not__acc__down, fact_self__append__conv2, fact__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096, fact_lists_Osimps, fact_xt1_I7_J, fact_order__trans, fact_restrict__extensional, fact_lexord__append__rightI, fact_single__valuedD, fact_const__Lin__Prof, fact_imageI, fact_butlast_Osimps_I1_J, fact_same__append__eq, fact_splitD_H, fact_lexord__trans, fact_lexord__irreflexive, fact_listrelp_ONil
% 89.82/23.48 % No. of inferences in proof: 1095
% 89.82/23.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 22946 ms resp. 22042 ms w/o parsing
% 92.66/24.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 92.66/24.06 % [INFO] Killing All external provers ...
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