%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT141+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 : n003.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 102.18s 25.95s
% Output : Refutation 104.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 525
% Syntax : Number of formulae : 1096 ( 252 unt; 0 typ; 2 def)
% Number of atoms : 3163 ( 875 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 31630 ( 432 ~; 156 |; 330 &;29153 @)
% ( 116 <=>;1443 =>; 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 : 102 ( 99 usr; 20 con; 0-6 aty)
% Number of variables : 4085 ( 0 ^;4032 !; 51 ?;4085 :)
% ( 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_c_____decl,type,
v_c____: $i ).
thf(c_Arrow__Order__Mirabelle_Obelow_decl,type,
c_Arrow__Order__Mirabelle_Obelow: $i ).
thf(v_P_____decl,type,
v_P____: $i ).
thf(v_b_____decl,type,
v_b____: $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(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(c_Lattices_Osemilattice__inf__class_Oinf_decl,type,
c_Lattices_Osemilattice__inf__class_Oinf: $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(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $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_Product__Type_OSigma_decl,type,
c_Product__Type_OSigma: $i > $i > $i > $i > $i ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_List_Olists_decl,type,
c_List_Olists: $i > $i > $i ).
thf(class_Lattices_Osemilattice__inf_decl,type,
class_Lattices_Osemilattice__inf: $i > $o ).
thf(c_List_Olistrel1_decl,type,
c_List_Olistrel1: $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_Onth_decl,type,
c_List_Onth: $i > $i > $i > $i ).
thf(c_List_OtakeWhile_decl,type,
c_List_OtakeWhile: $i > $i > $i > $i ).
thf(c_FuncSet_OPi_decl,type,
c_FuncSet_OPi: $i > $i > $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_List_Olist_Olist__case_decl,type,
c_List_Olist_Olist__case: $i > $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_Groups_Oplus__class_Oplus_decl,type,
c_Groups_Oplus__class_Oplus: $i > $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_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_FuncSet_Ocompose_decl,type,
c_FuncSet_Ocompose: $i > $i > $i > $i > $i > $i > $i ).
thf(c_List_Olistsp_decl,type,
c_List_Olistsp: $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_fequal_decl,type,
c_fequal: $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_Wellfounded_Oacc_decl,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $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_Product__Type_Ocurry_decl,type,
c_Product__Type_Ocurry: $i > $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_Arrow__Order__Mirabelle_Oabove_decl,type,
c_Arrow__Order__Mirabelle_Oabove: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omktop_decl,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(c_Relation_Oirrefl_decl,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(c_COMBS_decl,type,
c_COMBS: $i > $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(c_Relation_Orefl__on_decl,type,
c_Relation_Orefl__on: $i > $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] :
~ ( ( 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 )
=> ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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 ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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 )
=> ( 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(151,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
thf(1036,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(35,axiom,
tc_HOL_Obool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(629,plain,
tc_HOL_Obool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(147,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(1024,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)],[147]) ).
thf(427,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(2306,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)],[427]) ).
thf(387,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(2131,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)],[387]) ).
thf(519,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D2) ).
thf(2778,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(169,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(1105,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)],[169]) ).
thf(192,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(1237,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)],[192]) ).
thf(345,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(1899,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)],[345]) ).
thf(272,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(1549,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)],[272]) ).
thf(171,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(1110,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)],[171]) ).
thf(522,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD2) ).
thf(2787,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(485,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(2595,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)],[485]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD1) ).
thf(2544,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(121,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(941,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)],[121]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(977,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(158,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(1068,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(470,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(2527,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)],[470]) ).
thf(237,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(1401,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)],[237]) ).
thf(270,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(1544,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)],[270]) ).
thf(199,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(1269,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)],[199]) ).
thf(210,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(1305,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)],[210]) ).
thf(1,conjecture,
! [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 )
<=> ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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',conj_0) ).
thf(2,negated_conjecture,
~ ! [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 )
<=> ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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(neg_conjecture,[status(cth)],[1]) ).
thf(525,plain,
~ ! [A: $i] :
( ( ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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 )
=> ( 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 ) )
& ( ( 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 )
=> ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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)],[2]) ).
thf(526,plain,
~ ( ! [A: $i] :
( ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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 )
=> ( 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: $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 )
=> ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( A @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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(miniscope,[status(thm)],[525]) ).
thf(527,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_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk1 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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 ) )
& ( ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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 )
| ~ ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk1 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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 ) )
& ( ~ ( 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 ) )
& ( ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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 )
| ( 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(cnf,[status(esa)],[526]) ).
thf(528,plain,
( ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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 )
| ( 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(481,axiom,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(2581,plain,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(2582,plain,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL ) ),
inference(cnf,[status(esa)],[2581]) ).
thf(4590,plain,
! [A: $i] :
( ( ( 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 )
!= ( A @ hBOOL ) )
| ~ $true
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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(paramod_ordered,[status(thm)],[528,2582]) ).
thf(4591,plain,
! [A: $i] :
( ( ( v_b____ @ ( v_c____ @ ( sk1 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
!= ( A @ hBOOL ) )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[4590]) ).
thf(4592,plain,
( ~ ( v_b____ @ ( v_c____ @ ( sk1 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ ( c_fNot @ hAPP ) @ hBOOL )
| ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(pattern_uni,[status(thm)],[4591:[bind(A,$thf( 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 ) ))]]) ).
thf(257,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(1486,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)],[257]) ).
thf(183,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(1158,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)],[183]) ).
thf(467,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(2512,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)],[467]) ).
thf(62,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(730,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)],[62]) ).
thf(206,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(1290,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)],[206]) ).
thf(66,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(741,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)],[66]) ).
thf(160,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(1073,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ ( B @ ( B @ c_Set_Oimage ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(29,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(614,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)],[29]) ).
thf(48,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(677,plain,
! [A: $i,B: $i] :
( ( B @ c_List_Olist_ONil @ ( A @ ( B @ c_List_Osplice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(403,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(2195,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)],[403]) ).
thf(162,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(1078,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)],[162]) ).
thf(178,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(1137,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)],[178]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( B @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i] :
( ( F @ ( A @ hAPP ) @ ( G @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
!= ( G @ ( F @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaE) ).
thf(2607,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( B @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i] :
( ( F @ ( A @ hAPP ) @ ( G @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C
!= ( G @ ( F @ ( D @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(201,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(1275,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)],[201]) ).
thf(359,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(1988,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)],[359]) ).
thf(122,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(945,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)],[122]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__infI) ).
thf(2042,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(83,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(797,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)],[83]) ).
thf(430,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(2316,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)],[430]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( E @ ( A @ ( B @ c_List_Onth ) ) @ ( C @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( B @ c_List_OtakeWhile ) ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__takeWhile__less__P__nth) ).
thf(2434,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( E @ ( A @ ( B @ c_List_Onth ) ) @ ( C @ hAPP ) @ hBOOL ) )
=> ( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( B @ c_List_OtakeWhile ) ) @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(338,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(1872,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)],[338]) ).
thf(88,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(814,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)],[88]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(1327,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(318,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(1761,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)],[318]) ).
thf(110,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(913,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(262,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(1507,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)],[262]) ).
thf(117,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(930,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)],[117]) ).
thf(94,axiom,
tc_Nat_Onat @ class_Lattices_Olattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
thf(829,plain,
tc_Nat_Onat @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(372,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(2046,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)],[372]) ).
thf(336,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(1866,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(1867,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
inference(cnf,[status(esa)],[1866]) ).
thf(1868,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
inference(lifteq,[status(thm)],[1867]) ).
thf(1869,plain,
! [A: $i] : ( A @ ( A @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
inference(simp,[status(thm)],[1868]) ).
thf(5383,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)],[1869,2582]) ).
thf(5384,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
!= ( B @ hBOOL ) )
| ~ ( B @ ( c_fNot @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[5383]) ).
thf(5385,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_fequal @ hAPP ) @ hAPP ) @ ( c_fNot @ hAPP ) @ hBOOL ),
inference(pattern_uni,[status(thm)],[5384:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( c_fequal @ hAPP ) @ hAPP ) ))]]) ).
thf(5393,plain,
! [A: $i] :
~ ( A @ ( A @ ( c_fequal @ hAPP ) @ hAPP ) @ ( c_fNot @ hAPP ) @ hBOOL ),
inference(simp,[status(thm)],[5385]) ).
thf(56,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(709,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)],[56]) ).
thf(364,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(2020,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)],[364]) ).
thf(155,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(1046,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)],[155]) ).
thf(373,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(2082,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)],[373]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__iff) ).
thf(1529,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(342,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(1887,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)],[342]) ).
thf(241,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(1409,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)],[241]) ).
thf(15,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(570,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)],[15]) ).
thf(503,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(2698,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)],[503]) ).
thf(497,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(2667,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)],[497]) ).
thf(418,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1E) ).
thf(2269,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(218,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(1330,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)],[218]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__IntI) ).
thf(2682,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_List_Olists ) @ ( C @ ( D @ tc_List_Olist @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_List_Olistsp ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(203,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)],[203]) ).
thf(277,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(1577,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)],[277]) ).
thf(361,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(1992,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)],[361]) ).
thf(253,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(1462,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)],[253]) ).
thf(480,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(2571,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)],[480]) ).
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(20,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(587,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)],[20]) ).
thf(216,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(1323,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)],[216]) ).
thf(419,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(2274,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)],[419]) ).
thf(112,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(917,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)],[112]) ).
thf(54,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(702,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)],[54]) ).
thf(68,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(751,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)],[68]) ).
thf(118,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(934,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)],[118]) ).
thf(189,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(1191,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)],[189]) ).
thf(180,axiom,
( ( v_P____ @ ( v_F @ 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____ @ ( 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 ) @ ( v_F @ 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',fact_ab) ).
thf(1147,plain,
( ( ( 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 ) @ ( v_F @ 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_P____ @ ( v_F @ 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_P____ @ ( v_F @ 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____ @ ( 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 ) @ ( v_F @ 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)],[180]) ).
thf(305,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(1704,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)],[305]) ).
thf(515,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(2767,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)],[515]) ).
thf(288,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(1609,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)],[288]) ).
thf(26,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(606,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)],[26]) ).
thf(173,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(1115,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)],[173]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( ( 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(2158,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( ( 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)],[394]) ).
thf(366,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(2024,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)],[366]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__commute) ).
thf(2301,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__assoc) ).
thf(1362,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(442,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(2388,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)],[442]) ).
thf(89,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(817,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)],[89]) ).
thf(105,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(902,plain,
! [A: $i] : ( A @ c_List_Olist_ONil @ ( A @ c_List_Odistinct ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(194,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(1247,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)],[194]) ).
thf(476,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(2552,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)],[476]) ).
thf(142,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 @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( 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(1013,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 @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( 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)],[142]) ).
thf(77,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(770,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)],[77]) ).
thf(380,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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI) ).
thf(2105,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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(219,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(1334,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)],[219]) ).
thf(302,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(1682,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)],[302]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).
thf(1858,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
thf(1151,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__append__length) ).
thf(1677,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( A @ ( B @ ( D @ c_List_Olist_OCons @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_List_Oappend @ hAPP ) @ hAPP ) @ ( D @ c_List_Onth ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(477,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(2555,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)],[477]) ).
thf(126,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(966,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)],[126]) ).
thf(91,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(821,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)],[91]) ).
thf(363,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__idem) ).
thf(2017,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(374,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(2090,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)],[374]) ).
thf(21,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(591,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(153,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(1040,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)],[153]) ).
thf(289,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 @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).
thf(1632,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 @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(146,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(1020,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)],[146]) ).
thf(17,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(574,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)],[17]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Ocommute) ).
thf(1183,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) )
= ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__eq__cancel2) ).
thf(1283,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) )
= ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) ) ) )
& ( ( ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) )
= ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(185,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(1169,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)],[185]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntE) ).
thf(2371,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(265,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(1526,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)],[265]) ).
thf(137,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(998,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)],[137]) ).
thf(239,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(1405,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)],[239]) ).
thf(191,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(1201,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)],[191]) ).
thf(407,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(2205,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)],[407]) ).
thf(24,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(602,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)],[24]) ).
thf(132,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(981,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)],[132]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(766,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(100,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(877,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)],[100]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(692,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(249,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(1447,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)],[249]) ).
thf(124,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 @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb1) ).
thf(956,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 @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(324,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(1796,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)],[324]) ).
thf(471,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(2530,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)],[471]) ).
thf(335,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(1863,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)],[335]) ).
thf(294,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(1651,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(286,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(1604,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)],[286]) ).
thf(458,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(2473,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)],[458]) ).
thf(529,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(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(115,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(925,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)],[115]) ).
thf(396,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
thf(2164,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(761,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(384,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(2118,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)],[384]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
thf(1338,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(375,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oidem) ).
thf(2093,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(462,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(2496,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)],[462]) ).
thf(517,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaD1) ).
thf(2773,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(248,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(1438,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)],[248]) ).
thf(43,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(661,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)],[43]) ).
thf(211,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(1311,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)],[211]) ).
thf(412,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(2232,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)],[412]) ).
thf(484,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(2589,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)],[484]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) )
= ( A @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) @ ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Int__distrib1) ).
thf(2601,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) )
= ( A @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) @ ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(416,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(2249,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)],[416]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).
thf(2541,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(264,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(1519,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)],[264]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ! [D: $i] :
( ( C @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( C @ ( A @ c_List_Onth ) ) )
= ( D @ ( B @ ( A @ c_List_Onth ) ) ) ) )
& ( ( C @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__eq__iff__nth__eq) ).
thf(862,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( C @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( C @ ( A @ c_List_Onth ) ) )
= ( D @ ( B @ ( A @ c_List_Onth ) ) ) ) )
& ( ( C @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) ) )
=> ( C = B ) )
& ( ( C = B )
=> ( ! [D: $i] :
( ( C @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( C @ ( A @ c_List_Onth ) ) )
= ( D @ ( B @ ( A @ c_List_Onth ) ) ) ) )
& ( ( C @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( A @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(36,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(630,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)],[36]) ).
thf(447,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(2414,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)],[447]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D2) ).
thf(1387,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(309,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(1723,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)],[309]) ).
thf(109,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 @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb2) ).
thf(910,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 @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(509,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(2733,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)],[509]) ).
thf(223,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(1343,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)],[223]) ).
thf(278,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(1580,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)],[278]) ).
thf(420,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(2277,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)],[420]) ).
thf(260,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(1502,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)],[260]) ).
thf(315,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(1751,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)],[315]) ).
thf(90,axiom,
tc_HOL_Obool @ class_Lattices_Osemilattice__inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
thf(820,plain,
tc_HOL_Obool @ class_Lattices_Osemilattice__inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__commute) ).
thf(1457,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(325,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(1819,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)],[325]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Odistinct ) )
<=> ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ! [D: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C != D )
=> ( ( C @ ( A @ ( B @ c_List_Onth ) ) )
!= ( D @ ( A @ ( B @ c_List_Onth ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__conv__nth) ).
thf(830,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ! [D: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C != D )
=> ( ( C @ ( A @ ( B @ c_List_Onth ) ) )
!= ( D @ ( A @ ( B @ c_List_Onth ) ) ) ) ) ) )
=> ( A @ ( B @ c_List_Odistinct ) ) )
& ( ( A @ ( B @ c_List_Odistinct ) )
=> ! [C: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ! [D: $i] :
( ( A @ ( B @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C != D )
=> ( ( C @ ( A @ ( B @ c_List_Onth ) ) )
!= ( D @ ( A @ ( B @ c_List_Onth ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(148,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(1027,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)],[148]) ).
thf(383,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(2112,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)],[383]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( C @ ( D @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ c_Product__Type_OPair ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ c_COMBC ) ) @ hAPP ) @ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ tc_prod ) @ c_Set_Oimage ) ) ) )
= ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( D @ ( C @ c_Product__Type_OSigma ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_swap__product) ).
thf(2653,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( C @ ( D @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ c_Product__Type_OPair ) @ ( D @ ( C @ tc_prod ) @ ( D @ ( C @ c_COMBC ) ) @ hAPP ) @ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) @ hAPP ) @ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ tc_prod ) @ c_Set_Oimage ) ) ) )
= ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( D @ ( C @ c_Product__Type_OSigma ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(513,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(2758,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)],[513]) ).
thf(14,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(566,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)],[14]) ).
thf(328,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(1837,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)],[328]) ).
thf(285,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(1602,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)],[285]) ).
thf(228,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(1365,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)],[228]) ).
thf(498,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(2670,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)],[498]) ).
thf(355,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(1968,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)],[355]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(879,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 ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oassoc) ).
thf(1555,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(431,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(2332,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)],[431]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_List_Odistinct ) )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B @ ( C @ ( D @ c_List_Onth ) ) )
= ( A @ ( C @ ( D @ c_List_Onth ) ) ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__eq__iff__index__eq) ).
thf(889,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_List_Odistinct ) )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_List_Onth ) ) )
= ( A @ ( C @ ( D @ c_List_Onth ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_List_Onth ) ) )
= ( A @ ( C @ ( D @ c_List_Onth ) ) ) )
=> ( B = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(399,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(2179,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)],[399]) ).
thf(71,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(757,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)],[71]) ).
thf(435,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(2345,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(50,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(682,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)],[50]) ).
thf(408,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(2211,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)],[408]) ).
thf(240,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(1407,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)],[240]) ).
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(461,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(2492,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)],[461]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__assoc) ).
thf(1634,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).
thf(1392,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(226,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(1360,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)],[226]) ).
thf(378,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(2100,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)],[378]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
<=> ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( C @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__def) ).
thf(1970,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( C @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) ) )
& ( ( A @ ( B @ ( C @ c_Relation_Orefl__on ) ) )
=> ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( C @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__apply) ).
thf(2726,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(506,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(2724,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)],[506]) ).
thf(22,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(593,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)],[22]) ).
thf(417,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
thf(2266,plain,
v_a____ != v_b____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(2267,plain,
v_a____ != v_b____,
inference(polarity_switch,[status(thm)],[2266]) ).
thf(2268,plain,
v_b____ != v_a____,
inference(lifteq,[status(thm)],[2267]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( F @ c_Product__Type_OSigma ) ) ) @ ( B @ ( E @ ( C @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaI) ).
thf(1592,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( A @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( F @ c_Product__Type_OSigma ) ) ) @ ( B @ ( E @ ( C @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(18,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(578,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)],[18]) ).
thf(332,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(1856,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)],[332]) ).
thf(58,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(723,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(724,plain,
~ ? [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(miniscope,[status(thm)],[723]) ).
thf(725,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(cnf,[status(esa)],[724]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__commute) ).
thf(1096,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(465,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(2509,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)],[465]) ).
thf(297,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(1659,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)],[297]) ).
thf(37,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(637,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)],[37]) ).
thf(489,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 ) ) )
=> ~ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( A @ ( C @ c_List_Onth ) ) @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__length__takeWhile) ).
thf(2613,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 ) ) )
=> ~ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( A @ ( C @ c_List_Onth ) ) @ ( B @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(144,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 @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greatest) ).
thf(1016,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 @ hAPP ) @ hAPP ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(128,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 ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__trans) ).
thf(970,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 ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
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(2781,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(69,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(753,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( D @ ( A @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__Sigma__iff) ).
thf(2561,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( D @ ( A @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( A @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(33,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(622,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)],[33]) ).
thf(421,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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI2) ).
thf(2285,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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(195,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(1249,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)],[195]) ).
thf(231,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(1382,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)],[231]) ).
thf(198,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 @ hAPP ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb1) ).
thf(1266,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 @ hAPP ) @ hAPP ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(176,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(1131,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)],[176]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
thf(1668,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaD2) ).
thf(1874,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(284,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(1599,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)],[284]) ).
thf(308,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(1720,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)],[308]) ).
thf(357,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(1979,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)],[357]) ).
thf(512,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(2756,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)],[512]) ).
thf(317,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( B @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ ( B @ c_Relation_OId__on ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__subset__Times) ).
thf(1759,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( B @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ ( B @ c_Relation_OId__on ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(38,axiom,
tc_Nat_Onat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(647,plain,
tc_Nat_Onat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(321,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(1776,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)],[321]) ).
thf(454,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(2450,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)],[454]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( A @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaE2) ).
thf(1588,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( D @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( D @ ( A @ hAPP ) @ ( C @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(167,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(1099,plain,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(472,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(2536,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)],[472]) ).
thf(207,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(1297,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)],[207]) ).
thf(250,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(1451,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)],[250]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le2) ).
thf(2304,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(273,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(1552,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)],[273]) ).
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(2849,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)],[629,539]) ).
thf(2850,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)],[2849]) ).
thf(2851,plain,
! [A: $i] : ( A @ ( A @ ( tc_HOL_Obool @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(pattern_uni,[status(thm)],[2850:[bind(A,$thf( A )),bind(B,$thf( tc_HOL_Obool ))]]) ).
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_Oprod_Oprod__case ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__conv) ).
thf(2465,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)],[455]) ).
thf(362,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(2006,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)],[362]) ).
thf(57,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
thf(721,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(246,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(1434,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)],[246]) ).
thf(214,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(1318,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)],[214]) ).
thf(406,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(2203,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)],[406]) ).
thf(113,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(921,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)],[113]) ).
thf(330,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(1846,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)],[330]) ).
thf(511,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(2748,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)],[511]) ).
thf(438,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(2368,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)],[438]) ).
thf(159,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(1071,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)],[159]) ).
thf(344,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(1895,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)],[344]) ).
thf(401,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(2189,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)],[401]) ).
thf(530,plain,
( ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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 )
| ~ ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk1 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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(cnfConj,[status(thm)],[527]) ).
thf(123,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(953,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)],[123]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D1) ).
thf(2423,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(164,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(1086,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)],[164]) ).
thf(119,axiom,
v_F @ c_Arrow__Order__Mirabelle_OIIA,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I3_J) ).
thf(938,plain,
v_F @ c_Arrow__Order__Mirabelle_OIIA,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(475,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(2546,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)],[475]) ).
thf(514,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(2761,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)],[514]) ).
thf(46,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(674,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)],[46]) ).
thf(453,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(2440,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)],[453]) ).
thf(19,axiom,
tc_HOL_Obool @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(586,plain,
tc_HOL_Obool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(432,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(2338,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)],[432]) ).
thf(424,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(2292,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)],[424]) ).
thf(353,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(1959,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)],[353]) ).
thf(92,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(824,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)],[92]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__fun__def) ).
thf(1483,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(200,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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__greatest) ).
thf(1273,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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(271,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(1548,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)],[271]) ).
thf(208,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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI1) ).
thf(1301,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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(230,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(1374,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)],[230]) ).
thf(469,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(2524,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)],[469]) ).
thf(63,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(733,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)],[63]) ).
thf(385,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(2121,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)],[385]) ).
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 )
<=> ? [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(2235,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)],[413]) ).
thf(107,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(906,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)],[107]) ).
thf(508,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(2729,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)],[508]) ).
thf(293,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(1648,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)],[293]) ).
thf(311,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(1727,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)],[311]) ).
thf(263,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(1510,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)],[263]) ).
thf(31,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(618,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)],[31]) ).
thf(319,axiom,
! [A: $i] :
( ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ~ ~ ( A @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(1764,plain,
! [A: $i] :
( ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(443,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 @ hAPP ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__inf) ).
thf(2391,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(301,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(1680,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)],[301]) ).
thf(322,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(1784,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)],[322]) ).
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(2791,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(523,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 @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Relation_ORange ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Int__subset) ).
thf(2789,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 @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ c_Relation_ORange ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(460,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(2489,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)],[460]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).
thf(2568,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(67,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(743,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)],[67]) ).
thf(93,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(826,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)],[93]) ).
thf(238,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(1403,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)],[238]) ).
thf(388,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(2134,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)],[388]) ).
thf(106,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(904,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)],[106]) ).
thf(130,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(975,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)],[130]) ).
thf(502,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(2695,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)],[502]) ).
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(323,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(1786,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)],[323]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistsp ) )
= ( A @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__Int__eq) ).
thf(2220,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistsp ) )
= ( A @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ ( C @ tc_List_Olist @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(16,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(572,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)],[16]) ).
thf(428,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(2308,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)],[428]) ).
thf(28,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(611,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)],[28]) ).
thf(312,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(1733,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)],[312]) ).
thf(157,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(1058,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)],[157]) ).
thf(391,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(2148,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)],[391]) ).
thf(45,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__mono) ).
thf(672,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__commute) ).
thf(2521,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(104,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(900,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)],[104]) ).
thf(492,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(2642,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)],[492]) ).
thf(409,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(2214,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)],[409]) ).
thf(80,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_less__imp__le__nat) ).
thf(784,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)],[80]) ).
thf(141,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(1011,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)],[141]) ).
thf(64,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(736,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)],[64]) ).
thf(224,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(1349,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)],[224]) ).
thf(269,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(1542,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)],[269]) ).
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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).
thf(1144,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(30,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(616,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)],[30]) ).
thf(441,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(2378,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)],[441]) ).
thf(466,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(2510,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)],[466]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( C @ ( C @ c_Product__Type_OSigma ) ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OSigma ) ) ) @ ( 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__subset) ).
thf(764,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( C @ ( C @ c_Product__Type_OSigma ) ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( C @ c_List_Olists ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ c_Product__Type_OSigma ) ) ) @ ( 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)],[74]) ).
thf(25,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(604,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(49,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(680,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(681,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Relation_Otrans ) ),
inference(cnf,[status(esa)],[680]) ).
thf(331,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(1853,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)],[331]) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(990,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(136,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(996,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)],[136]) ).
thf(349,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(1933,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)],[349]) ).
thf(415,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb) ).
thf(2246,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(258,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(1492,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)],[258]) ).
thf(340,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(1877,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)],[340]) ).
thf(2808,plain,
( ( ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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 )
!= ( 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 ) )
| ~ $true
| ( 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____ @ ( 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(paramod_ordered,[status(thm)],[528,529]) ).
thf(2809,plain,
( ( ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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 )
!= ( 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(simp,[status(thm)],[2808]) ).
thf(2812,plain,
( ( ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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 ) )
!= ( 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 ) ) )
| ( 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(simp,[status(thm)],[2809]) ).
thf(386,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(2129,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)],[386]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) @ ( tc_HOL_Obool @ ( F @ ( C @ tc_prod ) @ 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_Times__subset__cancel2) ).
thf(2410,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) @ ( tc_HOL_Obool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) @ ( tc_HOL_Obool @ ( F @ ( C @ tc_prod ) @ 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)],[446]) ).
thf(521,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(2785,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)],[521]) ).
thf(186,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(1177,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)],[186]) ).
thf(351,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(1952,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)],[351]) ).
thf(172,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(1112,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)],[172]) ).
thf(84,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(799,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)],[84]) ).
thf(59,axiom,
tc_HOL_Obool @ class_Lattices_Olattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
thf(726,plain,
tc_HOL_Obool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(97,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(848,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)],[97]) ).
thf(53,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(700,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)],[53]) ).
thf(34,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(626,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)],[34]) ).
thf(111,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(915,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)],[111]) ).
thf(252,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(1460,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)],[252]) ).
thf(423,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(2289,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)],[423]) ).
thf(282,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(1594,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)],[282]) ).
thf(125,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(959,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)],[125]) ).
thf(76,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(768,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)],[76]) ).
thf(292,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(1643,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)],[292]) ).
thf(143,axiom,
v_F @ c_Arrow__Order__Mirabelle_Ounanimity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_u) ).
thf(1015,plain,
v_F @ c_Arrow__Order__Mirabelle_Ounanimity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(27,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(608,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)],[27]) ).
thf(12,axiom,
tc_Nat_Onat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(563,plain,
tc_Nat_Onat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(365,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(2022,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)],[365]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).
thf(1477,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(379,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(2101,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)],[379]) ).
thf(464,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(2506,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)],[464]) ).
thf(516,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(2770,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(133,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(983,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)],[133]) ).
thf(154,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(1044,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)],[154]) ).
thf(52,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(695,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)],[52]) ).
thf(193,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(1245,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)],[193]) ).
thf(459,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(2481,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)],[459]) ).
thf(414,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(2244,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)],[414]) ).
thf(138,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(1000,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)],[138]) ).
thf(98,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(851,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)],[98]) ).
thf(168,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(1102,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)],[168]) ).
thf(161,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(1076,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)],[161]) ).
thf(722,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(cnf,[status(esa)],[721]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( 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(1583,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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( 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)],[279]) ).
thf(376,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(2096,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)],[376]) ).
thf(531,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_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk1 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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(cnfConj,[status(thm)],[527]) ).
thf(457,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(2471,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)],[457]) ).
thf(347,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(1905,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)],[347]) ).
thf(202,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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI2) ).
thf(1277,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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(39,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(648,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)],[39]) ).
thf(87,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(812,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)],[87]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower2) ).
thf(1018,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(352,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(1958,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)],[352]) ).
thf(11,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(553,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)],[11]) ).
thf(127,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(968,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)],[127]) ).
thf(156,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(1049,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)],[156]) ).
thf(184,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(1166,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)],[184]) ).
thf(381,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(2107,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)],[381]) ).
thf(360,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(1990,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)],[360]) ).
thf(500,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(2684,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)],[500]) ).
thf(120,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(939,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)],[120]) ).
thf(222,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(1340,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)],[222]) ).
thf(444,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(2397,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)],[444]) ).
thf(402,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__idem) ).
thf(2192,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(196,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(1252,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)],[196]) ).
thf(65,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(739,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)],[65]) ).
thf(398,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(2175,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)],[398]) ).
thf(505,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(2720,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)],[505]) ).
thf(135,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(993,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)],[135]) ).
thf(78,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(776,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)],[78]) ).
thf(314,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(1748,plain,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(55,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(705,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)],[55]) ).
thf(440,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(2375,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)],[440]) ).
thf(496,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(2656,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)],[496]) ).
thf(358,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(1987,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)],[358]) ).
thf(291,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(1637,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)],[291]) ).
thf(188,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(1186,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)],[188]) ).
thf(152,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(1038,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)],[152]) ).
thf(197,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(1262,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)],[197]) ).
thf(268,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(1538,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)],[268]) ).
thf(371,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__mono) ).
thf(2044,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(313,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(1738,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)],[313]) ).
thf(220,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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI1) ).
thf(1336,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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(456,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(2468,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)],[456]) ).
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(225,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(1358,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)],[225]) ).
thf(463,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(2500,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)],[463]) ).
thf(320,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(1766,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)],[320]) ).
thf(41,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(656,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)],[41]) ).
thf(304,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(1702,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)],[304]) ).
thf(244,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(1427,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)],[244]) ).
thf(60,axiom,
tc_HOL_Obool @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(727,plain,
tc_HOL_Obool @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(165,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(1094,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)],[165]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Onth ) ) )
= ( D @ ( A @ ( C @ c_List_Onth ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__nth) ).
thf(1008,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ c_List_Onth ) ) )
= ( D @ ( A @ ( C @ c_List_Onth ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(2848,plain,
( ( ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) )
!= ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) ) )
| ( ( v_c____ @ ( 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 ) )
!= ( 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_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(simp,[status(thm)],[2812]) ).
thf(450,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(2426,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)],[450]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( D @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1I) ).
thf(1536,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( D @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(23,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(600,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)],[23]) ).
thf(390,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(2145,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)],[390]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ! [E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( E @ ( B @ ( D @ c_List_Onth ) ) @ ( E @ ( C @ ( D @ c_List_Onth ) ) @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__iff__nth) ).
thf(1940,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ! [E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( E @ ( B @ ( D @ c_List_Onth ) ) @ ( E @ ( C @ ( D @ c_List_Onth ) ) @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) ) )
=> ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_List_Olistrel ) @ ( B @ ( C @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( E @ ( B @ ( D @ c_List_Onth ) ) @ ( E @ ( C @ ( D @ c_List_Onth ) ) @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( C @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) )
= ( B @ ( D @ tc_List_Olist @ c_Nat_Osize__class_Osize ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(96,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(845,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)],[96]) ).
thf(329,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(1839,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)],[329]) ).
thf(354,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(1966,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)],[354]) ).
thf(72,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(759,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(174,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(1126,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)],[174]) ).
thf(400,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(2187,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)],[400]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le1) ).
thf(1108,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(491,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(2626,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)],[491]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
thf(1316,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(163,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(1084,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)],[163]) ).
thf(303,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(1685,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)],[303]) ).
thf(182,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(1157,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)],[182]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( C @ ( F @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2I) ).
thf(1321,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( C @ ( F @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(429,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(2310,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)],[429]) ).
thf(903,plain,
! [A: $i] : ( A @ c_List_Olist_ONil @ ( A @ c_List_Odistinct ) ),
inference(cnf,[status(esa)],[902]) ).
thf(436,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(2347,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)],[436]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2E) ).
thf(1412,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(382,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(2110,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)],[382]) ).
thf(234,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(1390,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)],[234]) ).
thf(434,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(2342,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)],[434]) ).
thf(276,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(1575,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)],[276]) ).
thf(518,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(2775,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)],[518]) ).
thf(232,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(1385,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)],[232]) ).
thf(397,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(2167,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)],[397]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) )
= ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Int__distrib2) ).
thf(1674,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) )
= ( A @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) @ ( B @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(40,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(652,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)],[40]) ).
thf(367,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(2026,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)],[367]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(786,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(79,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(781,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_List_Olist_ONil @ ( B @ c_List_Osplice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(448,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(2416,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)],[448]) ).
thf(103,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(896,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)],[103]) ).
thf(377,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(2098,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)],[377]) ).
thf(275,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(1558,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)],[275]) ).
thf(392,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(2152,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)],[392]) ).
thf(334,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(1861,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)],[334]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistsp ) )
= ( A @ ( C @ c_List_Olistsp ) @ ( B @ ( C @ c_List_Olistsp ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__inf__eq) ).
thf(1030,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_List_Olistsp ) )
= ( A @ ( C @ c_List_Olistsp ) @ ( B @ ( C @ c_List_Olistsp ) @ ( tc_HOL_Obool @ ( C @ tc_List_Olist @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(914,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ c_Relation_Otrans ) ),
inference(cnf,[status(esa)],[913]) ).
thf(445,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(2399,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)],[445]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) @ ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__Int__distrib1) ).
thf(2648,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) )
= ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) @ ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( C @ ( D @ ( E @ c_Product__Type_OSigma ) ) ) @ ( tc_HOL_Obool @ ( D @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(404,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(2198,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)],[404]) ).
thf(190,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(1193,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)],[190]) ).
thf(287,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(1607,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)],[287]) ).
thf(368,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(2036,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)],[368]) ).
thf(437,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(2362,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)],[437]) ).
thf(395,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)],[395]) ).
thf(510,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(2739,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)],[510]) ).
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(389,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(2142,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)],[389]) ).
thf(177,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(1133,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)],[177]) ).
thf(393,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(2155,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)],[393]) ).
thf(483,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(2587,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)],[483]) ).
thf(236,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(1395,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)],[236]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D1) ).
thf(2604,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntI) ).
thf(1303,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(316,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(1757,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)],[316]) ).
thf(255,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(1480,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)],[255]) ).
thf(4595,plain,
! [A: $i] :
( ( ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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 @ hBOOL ) )
| ~ $true
| ~ ( A @ ( c_fNot @ 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(paramod_ordered,[status(thm)],[528,2582]) ).
thf(4596,plain,
! [A: $i] :
( ( ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
!= ( A @ hBOOL ) )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ( v_b____ @ ( v_c____ @ ( sk1 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(simp,[status(thm)],[4595]) ).
thf(4597,plain,
( ~ ( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_b____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ ( c_fNot @ hAPP ) @ hBOOL )
| ( v_b____ @ ( v_c____ @ ( sk1 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( v_a____ @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(pattern_uni,[status(thm)],[4596:[bind(A,$thf( v_a____ @ ( v_b____ @ ( v_b____ @ ( v_c____ @ ( sk2 @ ( v_P____ @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_c____ @ ( 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 ) ))]]) ).
thf(422,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(2287,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)],[422]) ).
thf(32,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(620,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)],[32]) ).
thf(310,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(1725,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)],[310]) ).
thf(204,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(1280,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)],[204]) ).
thf(13,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(564,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)],[13]) ).
thf(247,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(1436,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)],[247]) ).
thf(405,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(2201,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)],[405]) ).
thf(212,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(1314,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)],[212]) ).
thf(296,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(1657,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)],[296]) ).
thf(86,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(807,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)],[86]) ).
thf(44,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(664,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)],[44]) ).
thf(411,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(2223,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)],[411]) ).
thf(369,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(2040,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)],[369]) ).
thf(433,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(2340,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)],[433]) ).
thf(494,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(2651,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)],[494]) ).
thf(82,axiom,
tc_Nat_Onat @ class_Lattices_Osemilattice__inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
thf(796,plain,
tc_Nat_Onat @ class_Lattices_Osemilattice__inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(116,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(928,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)],[116]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Onth ) ) )
= ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ c_List_Onth ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__nth) ).
thf(1033,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( D @ ( A @ ( B @ ( C @ c_List_OdropWhile ) ) @ ( C @ c_List_Onth ) ) )
= ( A @ ( B @ ( C @ c_List_OtakeWhile ) ) @ ( C @ tc_List_Olist @ c_Nat_Osize__class_Osize ) @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ c_List_Onth ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(306,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(1710,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)],[306]) ).
thf(504,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 )
<=> ( 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',fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096) ).
thf(2714,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)],[504]) ).
thf(343,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(1891,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)],[343]) ).
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(1059,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: $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 ) ) ) ) ) ),
inference(miniscope,[status(thm)],[1058]) ).
thf(1060,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
| ( E = D )
| ~ ( D @ ( E @ ( tc_HOL_Obool @ ( F @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( 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 ) ) ) ) ),
inference(cnf,[status(esa)],[1059]) ).
thf(1062,plain,
! [C: $i,B: $i,A: $i] :
( ( B != A )
| ~ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(cnfConj,[status(thm)],[1060]) ).
thf(1064,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
| ( B != A ) ),
inference(lifteq,[status(thm)],[1062]) ).
thf(1065,plain,
! [B: $i,A: $i] :
~ ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ),
inference(simp,[status(thm)],[1064]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( E @ ( E @ c_Product__Type_OSigma ) ) ) @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__subset__Sigma__aux) ).
thf(1930,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_COMBK ) ) @ ( A @ ( E @ ( E @ c_Product__Type_OSigma ) ) ) @ ( B @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower1) ).
thf(728,plain,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(326,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(1827,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)],[326]) ).
thf(482,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(2583,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)],[482]) ).
thf(108,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(908,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)],[108]) ).
thf(307,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(1713,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)],[307]) ).
thf(346,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(1902,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)],[346]) ).
thf(341,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(1885,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)],[341]) ).
thf(261,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(1505,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)],[261]) ).
thf(327,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(1829,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)],[327]) ).
thf(175,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(1129,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)],[175]) ).
thf(259,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(1500,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)],[259]) ).
thf(283,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(1597,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)],[283]) ).
thf(501,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(2687,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)],[501]) ).
thf(245,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 @ hAPP ) @ hAPP ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb2) ).
thf(1431,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 @ hAPP ) @ hAPP ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(139,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(1004,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)],[139]) ).
thf(85,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(803,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)],[85]) ).
thf(114,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(923,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)],[114]) ).
thf(42,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(659,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)],[42]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Relation_Otrans ) )
=> ( ( A @ ( C @ c_Relation_Otrans ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Relation_Otrans ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Int) ).
thf(2438,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Relation_Otrans ) )
=> ( ( A @ ( C @ c_Relation_Otrans ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Relation_Otrans ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(295,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(1653,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)],[295]) ).
thf(229,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(1367,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)],[229]) ).
thf(490,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(2615,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)],[490]) ).
thf(70,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(755,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)],[70]) ).
thf(47,axiom,
tc_Nat_Onat @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(676,plain,
tc_Nat_Onat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(243,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(1417,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)],[243]) ).
thf(337,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(1870,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)],[337]) ).
thf(129,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(972,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)],[129]) ).
thf(17872,plain,
$false,
inference(e,[status(thm)],[1036,629,1024,2306,2131,2778,1105,1237,1899,1549,1110,2787,2595,2544,941,977,1068,2527,1401,1544,1269,1305,4592,1486,1158,2512,730,1290,741,1073,614,677,2195,1078,1137,2607,1275,1988,945,2042,797,2316,2434,1872,814,1327,1761,913,1507,930,829,2046,5393,709,2020,1046,2082,1529,1887,1409,570,2698,2667,2269,1330,2682,1279,1577,1992,1462,2571,542,587,1323,2274,917,702,751,934,1191,1147,1704,2767,1609,606,1115,2158,2024,2301,1362,2388,817,902,1247,2552,1013,770,2105,1334,1682,1858,1151,1677,2555,966,821,2017,2090,591,1040,1632,1020,574,1183,1283,1169,2371,1526,998,1405,1201,2205,602,981,766,877,692,1447,956,1796,2530,1863,1651,1604,2473,529,546,925,2164,761,2118,1338,2093,2496,2773,1438,661,1311,2232,2589,2601,2249,2541,1519,862,630,2414,1387,1723,910,2733,1343,1580,2277,1502,1751,820,1457,1819,830,1027,2112,2653,2758,566,1837,1602,1365,2670,1968,879,1555,2332,889,2179,757,2345,682,2211,1407,551,2492,1634,1392,1360,2100,1970,2726,2724,593,2268,1592,578,1856,725,1096,2509,1659,637,2613,1016,970,2781,753,2561,622,2285,1249,1382,1266,1131,1668,1874,1599,1720,1979,2756,1759,647,1776,2450,1588,1099,2536,1297,1451,2304,1552,2851,2581,2465,2006,721,1434,1318,2203,921,1846,2748,2368,1071,1895,2189,530,953,2423,1086,938,2546,2761,674,2440,586,2338,2292,1959,824,1483,1273,1548,1301,1374,2524,733,2121,2235,906,2729,1648,1727,1510,618,1764,2391,1680,1784,2791,2789,2489,2568,743,826,1403,2134,904,975,2695,545,1786,2220,572,2308,611,1733,1058,2148,540,672,2521,900,2642,2214,784,1011,736,1349,1542,1144,616,2378,2510,764,604,681,1853,990,996,1933,2246,1492,1877,2812,2129,2410,2785,1177,1952,1112,799,726,848,700,626,915,1460,2289,1594,959,768,1643,1015,608,563,2022,1477,2101,2506,2770,983,1044,695,1245,2481,2244,1000,851,1102,1076,722,1583,2096,531,680,2471,1905,1277,648,812,1018,1958,553,968,2582,1049,1166,2107,1990,2684,939,1340,525,2397,2192,1252,739,2175,2720,993,776,1748,705,2375,2656,1987,1637,1186,1038,1869,1262,1538,2044,1738,1336,2468,544,1358,2500,1766,656,1702,1427,727,1094,1008,2848,2266,2426,1536,600,2145,1940,845,1839,1966,759,1126,2187,1108,2626,1316,1084,1685,539,1157,1321,2310,903,2347,1412,2110,1390,2342,1575,1866,2775,1385,2167,1674,652,2026,786,781,2416,896,2098,1558,2152,1861,1030,914,2399,2648,2198,1193,1607,2036,536,2362,2162,2739,549,2142,1133,2155,2587,1395,2604,1303,1757,1480,4597,2287,620,1725,1280,564,1436,2201,1314,1657,807,664,2223,2040,2340,2651,796,928,1033,1710,2714,1891,532,1065,1930,728,1827,528,2583,908,1713,1902,1885,1505,1829,1129,1500,723,1597,2687,1431,1004,803,923,659,543,2438,1653,1367,2615,755,676,1417,1870,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT141+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % 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
% 0.14/0.40 % Computer : n003.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 06:34:08 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.49/1.42 % [INFO] Parsing done (427ms).
% 2.49/1.44 % [INFO] Running in sequential loop mode.
% 3.39/1.74 % [INFO] eprover registered as external prover.
% 3.39/1.75 % [INFO] Scanning for conjecture ...
% 4.03/1.99 % [INFO] Found a conjecture (or negated_conjecture) and 522 axioms. Running axiom selection ...
% 5.87/2.31 % [INFO] Axiom selection finished. Selected 522 axioms (removed 0 axioms).
% 7.64/2.86 % [INFO] Problem is first-order (TPTP FOF).
% 8.07/2.90 % [INFO] Type checking passed.
% 8.07/2.91 % [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 ...
% 102.18/25.94 % External prover 'e' found a proof!
% 102.18/25.94 % [INFO] Killing All external provers ...
% 102.18/25.94 % Time passed: 25388ms (effective reasoning time: 24499ms)
% 102.18/25.94 % 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)>
% 102.18/25.95 % Axioms used in derivation (522): fact_order__le__neq__trans, fact_transI, fact_xt1_I1_J, fact_Pi__I, fact_converse__rtrancl__induct2, arity_fun__Orderings_Oorder, fact_Int__lower1, fact_dropWhile_Osimps_I2_J, fact_le__inf__iff, fact_single__valued__Id__on, fact_append__Nil2, fact_accp_Oequations, fact_inf2I, fact_lexord__append__leftI, fact_Range__Int__subset, fact_listrel1E, fact_lexord__lex, fact__C1_C, fact_last__appendR, arity_Nat__Onat__Lattices_Olattice, fact_le__eq__less__or__eq, fact_IIA__def, fact_funcset__image, fact_termination__basic__simps_I5_J, fact_unanimity__def, fact_curry__split, fact_list__eq__iff__nth__eq, fact_order__le__less__trans, fact_inf__sup__aci_I4_J, fact_inf_Oassoc, fact_nat__less__cases, fact_Pi__mono, fact_xt1_I4_J, fact_listrel__Cons1, fact_Cons__listrel1E2, fact_lists__IntI, fact_less__imp__le__nat, 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_in__mktop, fact_inf__absorb1, fact_in__mkbot, fact_linorder__neqE, fact_curryE, fact_leI, fact_Int__left__commute, fact_assms_I1_J, 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, fact_SigmaE2, fact_trans__Id__on, help_c__fconj__3, fact_image__Int__subset, fact_le__neq__implies__less, fact_length__takeWhile__less__P__nth, 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_less__infI2, 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_listrel__iff__nth, fact_split__paired__All, 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_takeWhile__nth, fact_le__fun__def, fact_acc__subset, fact_neq__if__length__neq, help_c__COMBS__1, fact_split__twice, fact_override__on__def, arity_fun__Lattices_Osemilattice__inf, fact_mem__splitE, 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_Int__assoc, fact_list_Osimps_I2_J, fact_in__measure, fact_listrelp__listrel__eq, fact_rtrancl__subset, fact_nth__length__takeWhile, 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_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_RangeI, fact_le__infI2, fact_nat__neq__iff, fact_nth__append__length, fact_Nil__notin__lex, 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_Times__Int__distrib1, arity_HOL__Obool__Orderings_Oord, fact__096a_A_126_061_Ab_096, fact_Id__onE, fact_RangeE, fact_Times__subset__cancel2, 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_converse__rtrancl__into__rtrancl, fact_pair__imageI, fact_inf2D2, fact_append__butlast__last__id, fact_same__fstI, fact_Id__on__subset__Times, fact_equalityD1, 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, 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_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_ab, fact_listrel__Nil1, fact_psubsetD, fact_le__iff__inf, fact_SigmaE, fact_Times__eq__cancel2, fact_listrel1__eq__len, fact_distinct__butlast, fact_set__eq__subset, fact_listsp_Osimps, fact_psubset__trans, 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_Pair__inject, fact_xt1_I12_J, fact_subset__refl, help_c__fNot__2, 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_inf__le1, fact_Sigma__Int__distrib2, 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_Int__commute, fact_less__le__not__le, fact_linorder__le__cases, fact_inf__apply, fact_assms_I3_J, fact_Id__on__eqI, fact_inf__mono, fact_in__measures_I2_J, fact_order__less__le__trans, fact_prod__caseI, fact_Sigma__Int__distrib1, arity_Nat__Onat__Orderings_Olinorder, fact_Nil2__notin__lex, fact_RangeP__Range__eq, fact_PiE, fact_rtrancl__induct2, fact_nat__le__linear, fact_mem__splitI2, fact_split__eta, fact_insert__Nil, fact_listrel1I2, fact_listrel__subset, help_c__COMBB__1, fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096, 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_order__less__asym, fact_override__on__apply__notin, fact_distinct__insert, fact_IntD2, 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_trancl__subset__Sigma__aux, fact_acc__downwards__aux, fact_list_Osimps_I5_J, fact_not__Cons__self2, fact_maps__simps_I1_J, fact_RangeP_Oequations, fact_rotate1__is__Nil__conv, fact_funcset__id, fact_trans__lex__prod, fact_SigmaI, fact_mem__Sigma__iff, fact_last__snoc, arity_HOL__Obool__Lattices_Osemilattice__inf, fact_rev__predicate2D, fact_transD, fact_single__valuedI, fact_le__refl, 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__eq__Cons__conv, fact_append__assoc, fact_in__lex__prod, fact_SigmaD2, fact_Domain__Id__on, fact_inf__sup__aci_I3_J, fact_last__ConsL, fact_in__measures_I1_J, fact_listrel__Nil2, fact_listrelp_Oequations_I1_J, fact_Int__absorb1, fact_listsp__inf__eq, fact_less__fun__def, fact_rev__predicate1D, fact_listrel__rtrancl__eq__rtrancl__listrel1, fact_trans__rtrancl, fact_inf_Oleft__idem, fact__096P_A_058_AProf_096, fact_xt1_I2_J, fact_rtrancl__listrel1__eq__len, fact_Pair__eq, 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_image__iff, fact_inf__assoc, fact_rtrancl_Ortrancl__into__rtrancl, fact_Lin__irrefl, fact_listrel1I1, fact_less__not__refl, fact_ord__eq__less__trans, fact_distinct__conv__nth, fact_append__in__listsp__conv, fact_le__trans, fact_inf__le2, help_c__COMBK__1, fact_equalityCE, fact_r__into__rtrancl, fact_dist, fact_Not__Domain__rtrancl, fact_image__eqI, fact_subsetD, 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_nat__add__commute, fact_Cons__eq__append__conv, fact_splice__Nil2, fact_swap__product, fact_partition_Osimps_I2_J, fact_image__ident, fact_partition_Osimps_I1_J, fact_impossible__Cons, fact_image__mono, fact_Cons__eq__appendI, fact_not__listrel1__Nil, fact_order__le__imp__less__or__eq, fact_acc__downward, fact_butlast__append, fact_takeWhile_Osimps_I2_J, fact_dictatorI, fact_eq__imp__le, fact_lexord__linear, fact_Nil__is__append__conv, fact_append__eq__append__conv2, fact_listrel__rtrancl__trans, fact_list_Osimps_I4_J, fact_dropWhile__nth, fact_curryI, fact_splice_Osimps_I1_J, fact_order__antisym__conv, fact_last__ConsR, fact_le__antisym, 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__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_refl__on__def, fact_Int__left__absorb, fact_order__less__imp__le, fact_nth__eq__iff__index__eq, fact_SigmaD1, fact_IntD1, fact_mem__def, fact_length__dropWhile__le, fact_inf__sup__aci_I1_J, fact_lists__Int__eq, fact_nat__less__le, 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_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
% 102.18/25.95 % No. of inferences in proof: 1094
% 102.18/25.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 25388 ms resp. 24499 ms w/o parsing
% 104.72/26.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 104.72/26.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------