%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT147+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 08:27:20 AM UTC 2026
% Result : Theorem 60.86s 28.83s
% Output : Refutation 63.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 524
% Syntax : Number of formulae : 1050 ( 207 unt; 0 typ; 0 def)
% Number of atoms : 3038 ( 614 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 31033 ( 356 ~; 84 |; 233 &;28689 @)
% ( 106 <=>;1565 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 105 ( 103 usr; 26 con; 0-6 aty)
% Number of variables : 3973 ( 0 ^;3935 !; 38 ?;3973 :)
% 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_b_____decl,type,
v_b____: $i ).
thf(v_a_____decl,type,
v_a____: $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_c_____decl,type,
v_c____: $i ).
thf(v_P_H_____decl,type,
v_P_H____: $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Orderings_Oord__class_Oless__eq_decl,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Orderings_Oord__class_Oless_decl,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(tc_Nat_Onat_decl,type,
tc_Nat_Onat: $i ).
thf(class_Lattices_Osemilattice__inf_decl,type,
class_Lattices_Osemilattice__inf: $i > $o ).
thf(c_Lattices_Osemilattice__inf__class_Oinf_decl,type,
c_Lattices_Osemilattice__inf__class_Oinf: $i > $i > $i > $i ).
thf(tc_HOL_Obool_decl,type,
tc_HOL_Obool: $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(class_Lattices_Olattice_decl,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Relation_ORange_decl,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_decl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(c_Wellfounded_Owf_decl,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(c_Wellfounded_Omlex__prod_decl,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(c_Relation_Oantisym_decl,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(c_Relation_OId__on_decl,type,
c_Relation_OId__on: $i > $i > $i ).
thf(c_Wellfounded_Omin__ext_decl,type,
c_Wellfounded_Omin__ext: $i > $i > $i ).
thf(c_Relation_ODomain_decl,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Wellfounded_Opred__nat_decl,type,
c_Wellfounded_Opred__nat: $i ).
thf(c_Fun_Ofun__upd_decl,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(c_Transitive__Closure_Ortranclp_decl,type,
c_Transitive__Closure_Ortranclp: $i > $i > $i ).
thf(c_Wellfounded_Oless__than_decl,type,
c_Wellfounded_Oless__than: $i ).
thf(c_Relation_Osingle__valued_decl,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(c_Relation_Orel__comp_decl,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_decl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_Wellfounded_Oacyclic_decl,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(c_FuncSet_Oextensional__funcset_decl,type,
c_FuncSet_Oextensional__funcset: $i > $i > $i > $i > $i ).
thf(c_FuncSet_OPi_decl,type,
c_FuncSet_OPi: $i > $i > $i > $i > $i ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_FuncSet_Oextensional_decl,type,
c_FuncSet_Oextensional: $i > $i > $i > $i ).
thf(c_Product__Type_Ocurry_decl,type,
c_Product__Type_Ocurry: $i > $i > $i > $i > $i ).
thf(c_Product__Type_Oprod_Oprod__case_decl,type,
c_Product__Type_Oprod_Oprod__case: $i > $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_FunDef_Opair__less_decl,type,
c_FunDef_Opair__less: $i ).
thf(c_Wellfounded_Olex__prod_decl,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_Wellfounded_OwfP_decl,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(c_Wellfounded_Oaccp_decl,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(c_FunDef_Oin__rel_decl,type,
c_FunDef_Oin__rel: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Ounanimity_decl,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
thf(c_Relation_Orefl__on_decl,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(c_fFalse_decl,type,
c_fFalse: $i ).
thf(c_Transitive__Closure_Otranclp_decl,type,
c_Transitive__Closure_Otranclp: $i > $i > $i ).
thf(c_Relation_Oinv__image_decl,type,
c_Relation_Oinv__image: $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_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_Recdef_Ocut_decl,type,
c_Recdef_Ocut: $i > $i > $i ).
thf(c_Nitpick_Owf__wfrec_H_decl,type,
c_Nitpick_Owf__wfrec_H: $i > $i > $i > $i > $i > $i ).
thf(c_Nitpick_Owf__wfrec_decl,type,
c_Nitpick_Owf__wfrec: $i > $i > $i > $i > $i ).
thf(c_Fun_Othe__inv__into_decl,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i > $i ).
thf(c_HOL_OThe_decl,type,
c_HOL_OThe: $i > $i > $i ).
thf(c_COMBS_decl,type,
c_COMBS: $i > $i > $i > $i ).
thf(c_fconj_decl,type,
c_fconj: $i ).
thf(c_Recdef_Owfrec_decl,type,
c_Recdef_Owfrec: $i > $i > $i > $i > $i ).
thf(c_COMBI_decl,type,
c_COMBI: $i > $i ).
thf(c_Recdef_Osame__fst_decl,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(c_Recdef_Oadm__wf_decl,type,
c_Recdef_Oadm__wf: $i > $i > $i > $i > $o ).
thf(c_Wellfounded_Omeasure_decl,type,
c_Wellfounded_Omeasure: $i > $i ).
thf(c_Predicate_ODomainP_decl,type,
c_Predicate_ODomainP: $i > $i > $i > $i > $o ).
thf(c_FuncSet_Ocompose_decl,type,
c_FuncSet_Ocompose: $i > $i > $i > $i > $i > $i > $i ).
thf(c_FuncSet_Orestrict_decl,type,
c_FuncSet_Orestrict: $i > $i > $i > $i > $i ).
thf(c_HOL_Oundefined_decl,type,
c_HOL_Oundefined: $i > $i ).
thf(c_Arrow__Order__Mirabelle_Oabove_decl,type,
c_Arrow__Order__Mirabelle_Oabove: $i > $i > $i > $i ).
thf(c_Relation_Oirrefl_decl,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(c_Arrow__Order__Mirabelle_Omktop_decl,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(c_FunDef_Orp__inv__image_decl,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(c_FunDef_Opair__leq_decl,type,
c_FunDef_Opair__leq: $i ).
thf(c_FunDef_Oreduction__pair_decl,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(c_FunDef_Omin__strict_decl,type,
c_FunDef_Omin__strict: $i ).
thf(c_FunDef_Omin__weak_decl,type,
c_FunDef_Omin__weak: $i ).
thf(c_Product__Type_Ointernal__split_decl,type,
c_Product__Type_Ointernal__split: $i > $i > $i > $i > $i > $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_fNot_decl,type,
c_fNot: $i ).
thf(c_Predicate_ORangeP_decl,type,
c_Predicate_ORangeP: $i > $i > $i > $i > $o ).
thf(c_Arrow__Order__Mirabelle_Odictator_decl,type,
c_Arrow__Order__Mirabelle_Odictator: $i > $i > $o ).
thf(c_Recdef_Owfrec__rel_decl,type,
c_Recdef_Owfrec__rel: $i > $i > $i > $i > $i > $i ).
thf(c_FunDef_Omax__weak_decl,type,
c_FunDef_Omax__weak: $i ).
thf(c_Product__Type_Oprod_Oprod__rec_decl,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Nitpick_Owfrec_H_decl,type,
c_Nitpick_Owfrec_H: $i > $i > $i > $i > $i > $i ).
thf(c_FunDef_Omax__strict_decl,type,
c_FunDef_Omax__strict: $i ).
thf(c_Nitpick_Orefl_H_decl,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(c_Relation_Ototal__on_decl,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(645,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Nitpick_Owf__wfrec_H ) ) ) ) )
= ( A @ ( A @ ( C @ ( B @ ( C @ ( D @ ( E @ c_Nitpick_Owf__wfrec ) ) ) @ ( D @ ( E @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Owf__wfrec_H__def) ).
thf(1322,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Nitpick_Owf__wfrec_H ) ) ) ) )
= ( A @ ( A @ ( C @ ( B @ ( C @ ( D @ ( E @ c_Nitpick_Owf__wfrec ) ) ) @ ( D @ ( E @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__less @ ( D @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omax__strict @ ( C @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omax__strict @ ( C @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smax__insertI) ).
thf(2452,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__less @ ( D @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omax__strict @ ( C @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omax__strict @ ( C @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Relation_Oantisym ) )
<=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__def) ).
thf(1337,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 )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = D ) ) )
=> ( A @ ( B @ c_Relation_Oantisym ) ) )
& ( ( A @ ( B @ c_Relation_Oantisym ) )
=> ! [C: $i,D: $i] :
( ( A @ ( D @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclp__trans) ).
thf(2094,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(74,axiom,
tc_HOL_Obool @ class_Lattices_Olattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
thf(760,plain,
tc_HOL_Obool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(455,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(2263,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)],[455]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( A @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( C @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) )
=> ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensionalityI) ).
thf(1559,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( A @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( C @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(332,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(1729,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)],[332]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(628,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntE) ).
thf(1840,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(358,axiom,
~ ( c_fFalse @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(1850,plain,
~ ( c_fFalse @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(512,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 ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__eta) ).
thf(2559,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 ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( B = A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(555,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F != E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) )
& ( ( F = E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
thf(1295,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F != E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) )
& ( ( F = E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(319,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_Otrancl ) @ ( 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__into__trancl1) ).
thf(1686,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_Otrancl ) @ ( 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)],[319]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) ) )
= ( A @ ( B @ ( c_fequal @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ c_HOL_OThe ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__def) ).
thf(1369,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Othe__inv__into ) ) ) ) )
= ( A @ ( B @ ( c_fequal @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( E @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( c_fconj @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ tc_fun ) @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( E @ c_HOL_OThe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(352,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downwards) ).
thf(1823,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(471,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(2336,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)],[471]) ).
thf(413,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(2109,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)],[413]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertCI) ).
thf(1454,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Orefl__on ) ) )
=> ( ( A @ ( B @ ( E @ c_Relation_Orefl__on ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( E @ c_Relation_Orefl__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Int) ).
thf(2412,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Orefl__on ) ) )
=> ( ( A @ ( B @ ( E @ c_Relation_Orefl__on ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( E @ c_Relation_Orefl__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(106,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(846,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)],[106]) ).
thf(178,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(1083,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)],[178]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le1) ).
thf(962,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower1) ).
thf(977,plain,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(299,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(1596,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)],[299]) ).
thf(66,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(730,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)],[66]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntI) ).
thf(1522,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
~ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( E @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__trancl__rD) ).
thf(2381,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
~ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( E @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(349,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(1808,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)],[349]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb1) ).
thf(994,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(518,axiom,
c_FunDef_Omax__weak @ ( c_FunDef_Omax__strict @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_FunDef_Oreduction__pair ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__rpair__set) ).
thf(2590,plain,
c_FunDef_Omax__weak @ ( c_FunDef_Omax__strict @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_FunDef_Oreduction__pair ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(741,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( C = B ) )
& ( ( C = B )
=> ( ( C @ ( B @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(394,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(2014,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)],[394]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
thf(1205,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(410,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(2099,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)],[410]) ).
thf(479,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(2380,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)],[479]) ).
thf(261,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(1437,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)],[261]) ).
thf(201,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(1158,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)],[201]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
thf(582,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__mono) ).
thf(762,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Wellfounded_Omeasure @ hAPP ) @ ( 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(1422,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 @ hAPP ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ c_Wellfounded_Omeasure @ hAPP ) @ ( 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)],[256]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
( ( A @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__tranclE) ).
thf(1939,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
( ( A @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(614,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( ( A = B )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclp__tranclp__tranclp) ).
thf(1692,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(176,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( A @ ( B @ c_Relation_Orefl__on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).
thf(1078,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( A @ ( B @ c_Relation_Orefl__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(524,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_Set_Oinsert ) ) @ ( D @ ( E @ c_Relation_ODomain ) ) )
= ( A @ ( D @ ( E @ c_Relation_ODomain ) ) @ ( C @ ( E @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__insert) ).
thf(2607,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_Set_Oinsert ) ) @ ( D @ ( E @ c_Relation_ODomain ) ) )
= ( A @ ( D @ ( E @ c_Relation_ODomain ) ) @ ( C @ ( E @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
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(533,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(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(550,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(333,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(1735,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)],[333]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclp_Ortrancl__into__rtrancl) ).
thf(1872,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(98,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(814,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)],[98]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( 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_trancl__trans) ).
thf(1988,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( 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)],[385]) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_FunDef_Orp__inv__image ) )
= ( A @ ( B @ c_Relation_Oinv__image ) @ ( A @ ( B @ c_Relation_Oinv__image ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ ( B @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ c_COMBS ) ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Oprod_Oprod__case ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp__inv__image__def) ).
thf(1640,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_FunDef_Orp__inv__image ) )
= ( A @ ( B @ c_Relation_Oinv__image ) @ ( A @ ( B @ c_Relation_Oinv__image ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ ( B @ ( A @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ c_COMBS ) ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ tc_prod ) @ ( B @ ( A @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Product__Type_Oprod_Oprod__case ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(400,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(2042,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)],[400]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_FunDef_Opair__less @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__lessI1) ).
thf(1497,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_FunDef_Opair__less @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(327,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(1705,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)],[327]) ).
thf(90,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(797,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)],[90]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( ( B @ ( A @ ( B @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ c_FunDef_Oreduction__pair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduction__pairI) ).
thf(2316,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( ( B @ ( A @ ( B @ ( C @ ( C @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ c_FunDef_Oreduction__pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__rtranclp) ).
thf(1507,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( A @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(129,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_Transitive__Closure_Ortranclp ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Transitive__Closure_Ortranclp ) )
= ( B @ ( C @ c_Transitive__Closure_Ortranclp ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclp__subset) ).
thf(930,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_Transitive__Closure_Ortranclp ) @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ c_Transitive__Closure_Ortranclp ) )
= ( B @ ( C @ c_Transitive__Closure_Ortranclp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(475,axiom,
! [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_c____ @ ( v_a____ @ ( 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 ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ 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__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096) ).
thf(2360,plain,
! [A: $i] :
( ( ( v_c____ @ ( v_a____ @ ( 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 ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ 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 )
=> ( 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_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_c____ @ ( v_a____ @ ( 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 ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ 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)],[475]) ).
thf(180,axiom,
! [A: $i] : ( c_fFalse @ ( A @ ( tc_HOL_Obool @ c_COMBK ) ) @ ( A @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBK ) ) @ ( A @ c_Wellfounded_OwfP ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__empty) ).
thf(1095,plain,
! [A: $i] : ( c_fFalse @ ( A @ ( tc_HOL_Obool @ c_COMBK ) ) @ ( A @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_COMBK ) ) @ ( A @ c_Wellfounded_OwfP ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_COMBI @ ( D @ ( D @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( D @ ( D @ ( E @ c_FuncSet_Ocompose ) ) ) ) ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__compose) ).
thf(1746,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ c_COMBI @ ( D @ ( D @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( D @ ( D @ ( E @ c_FuncSet_Ocompose ) ) ) ) ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(192,axiom,
tc_Nat_Onat @ class_Lattices_Olattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
thf(1127,plain,
tc_Nat_Onat @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ~ ( B @ ( A @ ( A @ ( 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_wf__not__refl) ).
thf(2227,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ~ ( B @ ( A @ ( A @ ( 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)],[443]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D2) ).
thf(1441,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert ) ) @ ( D @ c_Wellfounded_Owf ) )
<=> ( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Wellfounded_Owf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__insert) ).
thf(1645,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Wellfounded_Owf ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert ) ) @ ( D @ c_Wellfounded_Owf ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert ) ) @ ( D @ c_Wellfounded_Owf ) )
=> ( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Wellfounded_Owf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Wellfounded_Omlex__prod ) ) )
= ( C @ c_COMBI @ ( B @ ( C @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ ( C @ ( C @ ( tc_Nat_Onat @ tc_prod ) @ ( C @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ tc_prod ) @ ( C @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Wellfounded_Oless__than @ ( C @ ( tc_Nat_Onat @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( C @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__prod__def) ).
thf(1529,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Wellfounded_Omlex__prod ) ) )
= ( C @ c_COMBI @ ( B @ ( C @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ ( C @ ( C @ ( tc_Nat_Onat @ tc_prod ) @ ( C @ tc_fun ) @ ( tc_Nat_Onat @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ tc_prod ) @ ( C @ ( C @ c_COMBS ) ) @ hAPP ) @ hAPP ) @ ( A @ ( c_Wellfounded_Oless__than @ ( C @ ( tc_Nat_Onat @ c_Wellfounded_Olex__prod ) ) ) @ ( C @ ( C @ ( tc_Nat_Onat @ tc_prod ) @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( E @ ( F @ c_Set_Oinsert ) ) @ ( C @ ( F @ c_FuncSet_Oextensional__funcset ) ) ) @ ( B @ ( C @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( F @ c_FuncSet_Oextensional__funcset ) ) ) @ ( C @ c_HOL_Oundefined @ ( E @ ( B @ ( C @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( C @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__restrict__domain) ).
thf(1703,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( E @ ( F @ c_Set_Oinsert ) ) @ ( C @ ( F @ c_FuncSet_Oextensional__funcset ) ) ) @ ( B @ ( C @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( F @ c_FuncSet_Oextensional__funcset ) ) ) @ ( C @ c_HOL_Oundefined @ ( E @ ( B @ ( C @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( C @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(218,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(1228,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)],[218]) ).
thf(430,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(2173,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)],[430]) ).
thf(13,axiom,
tc_Nat_Onat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(565,plain,
tc_Nat_Onat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left__if1) ).
thf(1430,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
thf(1760,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ ( E @ ( F @ tc_prod ) @ c_member @ ( E @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( F @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ ( E @ ( F @ tc_prod ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ c_COMBC ) ) @ ( F @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( F @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( tc_HOL_Obool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).
thf(587,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(513,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(2562,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)],[513]) ).
thf(355,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(1832,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)],[355]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( D @ ( B @ ( C @ ( E @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrictI) ).
thf(2356,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( D @ ( B @ ( C @ ( E @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(493,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(2444,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)],[493]) ).
thf(219,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(1264,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)],[219]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Orefl__on ) ) )
=> ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD2) ).
thf(1511,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Orefl__on ) ) )
=> ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(58,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)],[58]) ).
thf(433,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(2185,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)],[433]) ).
thf(293,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(1577,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)],[293]) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__unfold__right) ).
thf(1059,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( F @ ( D @ ( G @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( F @ ( G @ c_Relation_Orel__comp ) ) ) ) )
= ( A @ ( B @ ( E @ ( F @ ( D @ c_Relation_Orel__comp ) ) ) ) @ ( C @ ( E @ ( D @ ( G @ c_Relation_Orel__comp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_O__assoc) ).
thf(1132,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( F @ ( D @ ( G @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( F @ ( G @ c_Relation_Orel__comp ) ) ) ) )
= ( A @ ( B @ ( E @ ( F @ ( D @ c_Relation_Orel__comp ) ) ) ) @ ( C @ ( E @ ( D @ ( G @ c_Relation_Orel__comp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(488,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(2420,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)],[488]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).
thf(853,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Recdef_Oadm__wf ) ) ) )
=> ( ( C @ ( E @ c_Wellfounded_Owf ) )
=> ? [F: $i] :
( ! [G: $i] :
( ( G @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL )
=> ( G = F ) )
& ( F @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfrec__unique) ).
thf(2403,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Recdef_Oadm__wf ) ) ) )
=> ( ( C @ ( E @ c_Wellfounded_Owf ) )
=> ? [F: $i] :
( ! [G: $i] :
( ( G @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL )
=> ( G = F ) )
& ( F @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(197,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(1147,plain,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(143,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(969,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)],[143]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI1) ).
thf(770,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(291,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 )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclE) ).
thf(1568,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 )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(396,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 ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) ) @ ( 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__twice) ).
thf(2024,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 ) @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_Oprod_Oprod__case ) ) ) @ ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(505,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_Otrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( 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__trancl__trancl) ).
thf(2533,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_Otrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( 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)],[505]) ).
thf(127,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__unfold__left) ).
thf(924,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(380,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(1946,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)],[380]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( B @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ ( B @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclp__into__tranclp2) ).
thf(1664,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( B @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ ( B @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left__if0) ).
thf(2105,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(416,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ c_HOL_OThe ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__sym__eq__trivial) ).
thf(2122,plain,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ c_HOL_OThe ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb1) ).
thf(937,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
thf(2324,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_FunDef_Opair__less @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__lessI2) ).
thf(2027,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_FunDef_Opair__less @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(447,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_HOL_OThe ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__eq__trivial) ).
thf(2236,plain,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ ( tc_HOL_Obool @ ( B @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_HOL_OThe ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(623,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(244,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(1383,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)],[244]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
<=> ( A @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( B @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__comp__self) ).
thf(1020,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) )
& ( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( B @ c_Wellfounded_Owf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(574,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(381,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(1960,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)],[381]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Wellfounded_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__acyclic) ).
thf(806,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Wellfounded_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Otrancl ) @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq) ).
thf(1169,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Otrancl ) @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Otrancl ) @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(242,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(1377,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)],[242]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_Set_Oinsert ) ) )
= ( A @ ( B @ ( C @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(956,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_Set_Oinsert ) ) )
= ( A @ ( B @ ( C @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(174,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(1072,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)],[174]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ c_COMBI @ ( B @ ( C @ ( D @ c_Recdef_Ocut ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ c_COMBS ) ) @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ ( D @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_fun ) @ ( D @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Recdef_Oadm__wf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adm__lemma) ).
thf(1394,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( D @ c_COMBI @ ( B @ ( C @ ( D @ c_Recdef_Ocut ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( D @ c_COMBS ) ) @ ( C @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ ( D @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ ( D @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ tc_fun ) @ ( D @ ( D @ tc_fun ) @ ( C @ ( D @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Recdef_Oadm__wf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ hAPP ) @ hBOOL )
| ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).
thf(1351,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( B @ hAPP ) @ hBOOL )
| ( C = A ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__commute) ).
thf(660,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( A @ ( C @ ( B @ ( D @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__inv__image) ).
thf(1433,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( A @ ( C @ ( B @ ( D @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D1) ).
thf(1405,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(116,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(877,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)],[116]) ).
thf(54,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(692,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)],[54]) ).
thf(435,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(2190,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)],[435]) ).
thf(378,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(1943,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)],[378]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__subset) ).
thf(1201,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(482,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(2392,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)],[482]) ).
thf(425,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(2154,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)],[425]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1E) ).
thf(1696,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ~ ( B @ ( A @ ( A @ ( 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_wf__irrefl) ).
thf(2586,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ~ ( B @ ( A @ ( A @ ( 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)],[516]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( B @ ( G @ ( D @ c_FuncSet_Oextensional__funcset ) ) ) @ ( C @ ( G @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( G @ ( D @ c_FuncSet_Oextensional__funcset ) ) ) @ ( F @ ( A @ ( C @ ( G @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ ( G @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__extend__domainI) ).
thf(1863,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( E @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( B @ ( G @ ( D @ c_FuncSet_Oextensional__funcset ) ) ) @ ( C @ ( G @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( E @ ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( G @ ( D @ c_FuncSet_Oextensional__funcset ) ) ) @ ( F @ ( A @ ( C @ ( G @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ ( G @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(125,axiom,
( c_Wellfounded_Oless__than
= ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Otrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__than__def) ).
thf(920,plain,
( c_Wellfounded_Oless__than
= ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Otrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(498,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(2473,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)],[498]) ).
thf(7,axiom,
tc_Nat_Onat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(546,plain,
tc_Nat_Onat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI2) ).
thf(810,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(269,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(1470,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)],[269]) ).
thf(347,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(1783,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)],[347]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).
thf(1636,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( 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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).
thf(1153,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( 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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(75,axiom,
tc_HOL_Obool @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(761,plain,
tc_HOL_Obool @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(228,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(1311,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)],[228]) ).
thf(463,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__less @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omin__strict @ ( A @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omin__strict @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert ) ) @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smin__insertI) ).
thf(2296,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__less @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omin__strict @ ( A @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omin__strict @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert ) ) @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(403,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(2083,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)],[403]) ).
thf(500,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 )
=> ( ( ( B @ ( C @ ( D @ c_Set_Oinsert ) ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert ) ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(2496,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 )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Set_Oinsert ) ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Set_Oinsert ) ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(165,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) ) ) )
= ( A @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__comp__rtrancl__eq) ).
thf(1047,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) ) ) )
= ( A @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI2) ).
thf(1057,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( 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_Otrancl ) @ ( 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_trancl__rtrancl__trancl) ).
thf(1274,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( 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_Otrancl ) @ ( 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)],[221]) ).
thf(330,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(1723,plain,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(522,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(2601,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).
thf(825,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(450,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_Otrancl ) @ ( 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__into__trancl2) ).
thf(2249,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_Otrancl ) @ ( 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)],[450]) ).
thf(294,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(1580,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)],[294]) ).
thf(111,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(862,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)],[111]) ).
thf(215,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(1217,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)],[215]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ c_Wellfounded_Owf ) )
=> ! [E: $i] :
( ( E @ ( C @ ( D @ ( A @ ( B @ c_Recdef_Owfrec ) ) ) @ hAPP ) )
= ( E @ ( E @ ( D @ ( C @ ( D @ ( A @ ( B @ c_Recdef_Owfrec ) ) ) @ ( A @ ( B @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__wfrec) ).
thf(1666,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ c_Wellfounded_Owf ) )
=> ! [E: $i] :
( ( E @ ( C @ ( D @ ( A @ ( B @ c_Recdef_Owfrec ) ) ) @ hAPP ) )
= ( E @ ( E @ ( D @ ( C @ ( D @ ( A @ ( B @ c_Recdef_Owfrec ) ) ) @ ( A @ ( B @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(272,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(1487,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)],[272]) ).
thf(369,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(1883,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)],[369]) ).
thf(137,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(952,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)],[137]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I) ).
thf(2541,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( B @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(85,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(788,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)],[85]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
<=> ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
thf(1619,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(424,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(2150,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)],[424]) ).
thf(420,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_OwfP ) )
<=> ! [C: $i] : ( C @ ( A @ ( B @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).
thf(2132,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( C @ ( A @ ( B @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Wellfounded_OwfP ) ) )
& ( ( A @ ( B @ c_Wellfounded_OwfP ) )
=> ! [C: $i] : ( C @ ( A @ ( B @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(487,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(2414,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)],[487]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__idem) ).
thf(566,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_FunDef_Oin__rel ) ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( 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(2179,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 ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_FunDef_Oin__rel ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( 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)],[432]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).
thf(682,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_OwfP ) )
=> ( A @ ( B @ c_Transitive__Closure_Otranclp ) @ ( B @ c_Wellfounded_OwfP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__trancl) ).
thf(1106,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_OwfP ) )
=> ( A @ ( B @ c_Transitive__Closure_Otranclp ) @ ( B @ c_Wellfounded_OwfP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__assoc) ).
thf(625,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_Oextensional__funcset ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ hAPP ) )
= ( E @ c_HOL_Oundefined ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__arb) ).
thf(2433,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_Oextensional__funcset ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ hAPP ) )
= ( E @ c_HOL_Oundefined ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(438,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(2200,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)],[438]) ).
thf(103,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(830,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)],[103]) ).
thf(465,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(2313,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)],[465]) ).
thf(193,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(1128,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)],[193]) ).
thf(509,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( B @ ( C @ ( D @ ( E @ c_Recdef_Owfrec ) ) ) ) )
=> ( ( C @ ( E @ c_Wellfounded_Owf ) )
=> ( ( A @ ( F @ hAPP ) )
= ( A @ ( A @ ( C @ ( F @ ( D @ ( E @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__wfrec) ).
thf(2547,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( B @ ( C @ ( D @ ( E @ c_Recdef_Owfrec ) ) ) ) )
=> ( ( C @ ( E @ c_Wellfounded_Owf ) )
=> ( ( A @ ( F @ hAPP ) )
= ( A @ ( A @ ( C @ ( F @ ( D @ ( E @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( B @ c_HOL_Oundefined ) ) )
& ( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__apply) ).
thf(2344,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( B @ c_HOL_Oundefined ) ) )
& ( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(18,axiom,
tc_HOL_Obool @ class_Lattices_Osemilattice__inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
thf(578,plain,
tc_HOL_Obool @ class_Lattices_Osemilattice__inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__inf__iff) ).
thf(697,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(426,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(2157,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)],[426]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) ) ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__idemp__self__comp) ).
thf(1017,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( B @ c_Relation_Orel__comp ) ) ) ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(232,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_Set_Oinsert ) ) @ ( D @ ( E @ c_Relation_ORange ) ) )
= ( A @ ( D @ ( E @ c_Relation_ORange ) ) @ ( B @ ( D @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__insert) ).
thf(1328,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_Set_Oinsert ) ) @ ( D @ ( E @ c_Relation_ORange ) ) )
= ( A @ ( D @ ( E @ c_Relation_ORange ) ) @ ( B @ ( D @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__inter__insert) ).
thf(1111,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_OwfP ) )
=> ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__wfPD) ).
thf(1672,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_OwfP ) )
=> ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(154,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(1006,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)],[154]) ).
thf(113,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(869,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)],[113]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ ( C @ ( F @ c_Fun_Ooverride__on ) ) ) ) ) )
= ( E @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_override__on__apply__in) ).
thf(1755,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ ( C @ ( F @ c_Fun_Ooverride__on ) ) ) ) ) )
= ( E @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infE) ).
thf(1118,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ~ ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(650,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Opreorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(136,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(948,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)],[136]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_COMBI @ ( E @ ( E @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( B @ ( D @ ( E @ ( E @ c_FuncSet_Ocompose ) ) ) ) ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__Id) ).
thf(1856,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( E @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( D @ ( E @ c_FuncSet_OPi ) ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_COMBI @ ( E @ ( E @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( B @ ( D @ ( E @ ( E @ c_FuncSet_Ocompose ) ) ) ) ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(64,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(725,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)],[64]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Recdef_Oadm__wf ) ) ) )
<=> ! [E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( B @ ( G @ ( H @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( H @ ( E @ hAPP ) )
= ( H @ ( F @ hAPP ) ) ) )
=> ( ( G @ ( E @ ( A @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( A @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adm__wf__def) ).
thf(2460,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( B @ ( G @ ( H @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( H @ ( E @ hAPP ) )
= ( H @ ( F @ hAPP ) ) ) )
=> ( ( G @ ( E @ ( A @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( A @ hAPP ) @ hAPP ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Recdef_Oadm__wf ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Recdef_Oadm__wf ) ) ) )
=> ! [E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( B @ ( G @ ( H @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( H @ ( E @ hAPP ) )
= ( H @ ( F @ hAPP ) ) ) )
=> ( ( G @ ( E @ ( A @ hAPP ) @ hAPP ) )
= ( G @ ( F @ ( A @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(161,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(1028,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)],[161]) ).
thf(237,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(1361,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)],[237]) ).
thf(130,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(933,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)],[130]) ).
thf(175,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(1075,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)],[175]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(637,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(350,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(1810,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)],[350]) ).
thf(412,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(2108,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)],[412]) ).
thf(11,axiom,
tc_Nat_Onat @ class_Lattices_Osemilattice__inf,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
thf(554,plain,
tc_Nat_Onat @ class_Lattices_Osemilattice__inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(71,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(753,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2E) ).
thf(1739,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
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(537,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(402,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__fun__def) ).
thf(2080,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(642,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(254,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(1414,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)],[254]) ).
thf(1,conjecture,
! [A: $i] :
( ( v_c____ @ ( v_a____ @ ( 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 ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ 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_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',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( v_c____ @ ( v_a____ @ ( 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 ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ 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_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(neg_conjecture,[status(cth)],[1]) ).
thf(526,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 )
=> ( v_c____ @ ( v_a____ @ ( 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 ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ 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 ) )
& ( ( v_c____ @ ( v_a____ @ ( 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 ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ 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_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)],[2]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Oacyclic ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Wellfounded_Oacyclic ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__subset) ).
thf(2551,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Oacyclic ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Wellfounded_Oacyclic ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(404,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(2085,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)],[404]) ).
thf(213,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(1207,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)],[213]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(590,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(200,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(1155,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)],[200]) ).
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(547,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(336,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD1) ).
thf(1744,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D1) ).
thf(1150,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(654,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ? [E: $i] :
( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ ( D @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclp_Oequations_I2_J) ).
thf(1974,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ? [E: $i] :
( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ ( D @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( A = B ) )
=> ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ? [E: $i] :
( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ ( D @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(166,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(1050,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)],[166]) ).
thf(367,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_Relation_Oantisym ) )
=> ( B @ ( C @ c_Relation_Oantisym ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__subset) ).
thf(1874,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_Relation_Oantisym ) )
=> ( B @ ( C @ c_Relation_Oantisym ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(569,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(422,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(2140,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)],[422]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__idem) ).
thf(605,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(353,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(1825,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( E @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) ) )
<=> ! [G: $i] :
( ( C @ ( B @ ( G @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( D @ hAPP ) )
= ( G @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cuts__eq) ).
thf(2285,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i] :
( ( C @ ( B @ ( G @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( D @ hAPP ) )
= ( G @ ( A @ hAPP ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( E @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ ( E @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) ) )
=> ! [G: $i] :
( ( C @ ( B @ ( G @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( D @ hAPP ) )
= ( G @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
thf(1114,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__commute) ).
thf(647,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(150,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(997,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)],[150]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD) ).
thf(2125,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
=> ( ( C @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(297,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(1588,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)],[297]) ).
thf(147,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(985,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)],[147]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_OwfP ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Wellfounded_OwfP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__subset) ).
thf(1002,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_OwfP ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Wellfounded_OwfP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(359,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(1852,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)],[359]) ).
thf(229,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(1318,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)],[229]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Transitive__Closure_Ortranclp ) @ ( B @ ( C @ c_Transitive__Closure_Ortranclp ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclp__mono) ).
thf(792,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Transitive__Closure_Ortranclp ) @ ( B @ ( C @ c_Transitive__Closure_Ortranclp ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(345,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(1779,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)],[345]) ).
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(541,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(268,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(1466,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)],[268]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) )
= C )
<=> ( ( B @ ( C @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
thf(1286,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( B @ ( C @ hAPP ) )
= A )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) )
= C ) )
& ( ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) )
= C )
=> ( ( B @ ( C @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI) ).
thf(1035,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( A @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD2) ).
thf(2408,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( A @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(311,axiom,
c_FunDef_Omin__weak @ ( c_FunDef_Omin__strict @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_FunDef_Oreduction__pair ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__rpair__set) ).
thf(1663,plain,
c_FunDef_Omin__weak @ ( c_FunDef_Omin__strict @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_FunDef_Oreduction__pair ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(406,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( C @ ( F @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2I) ).
thf(2089,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( C @ ( F @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI) ).
thf(1026,plain,
! [A: $i,B: $i,C: $i] : ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(371,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(1895,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)],[371]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( C @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( E @ ( F @ c_Fun_Ofun__upd ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ c_Fun_Ofun__upd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__upd) ).
thf(773,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( C @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( E @ ( F @ c_Fun_Ofun__upd ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ c_Fun_Ofun__upd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__trancl) ).
thf(794,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD2) ).
thf(1996,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(489,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(2423,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)],[489]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortranclp ) @ ( B @ c_Transitive__Closure_Ortranclp ) )
= ( A @ ( B @ c_Transitive__Closure_Ortranclp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclp__idemp) ).
thf(888,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortranclp ) @ ( B @ c_Transitive__Closure_Ortranclp ) )
= ( A @ ( B @ c_Transitive__Closure_Ortranclp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(122,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(906,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)],[122]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( F @ ( C @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( D @ ( A @ hAPP ) @ ( E @ ( A @ hAPP ) @ ( 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__inv__image) ).
thf(1135,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( D @ ( A @ hAPP ) @ ( E @ ( A @ hAPP ) @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( F @ ( C @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( F @ ( C @ c_Relation_Oinv__image ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP ) @ ( E @ ( A @ hAPP ) @ ( 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)],[195]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( A @ ( B @ ( C @ ( D @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__extensional) ).
thf(2001,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( A @ ( B @ ( C @ ( D @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(142,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(965,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)],[142]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) )
= ( D @ c_HOL_Oundefined ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__arb) ).
thf(2176,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( C @ ( D @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) )
= ( D @ c_HOL_Oundefined ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [E: $i] : ( A @ ( E @ ( C @ ( B @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__iff) ).
thf(1680,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( A @ ( E @ ( C @ ( B @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] : ( A @ ( E @ ( C @ ( B @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).
thf(1103,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Transitive__Closure_Otrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(216,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 )
=> ( ( D @ ( A @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i] :
( ( B @ ( G @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ hBOOL ) ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__induct) ).
thf(1219,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 )
=> ( ( D @ ( A @ hAPP ) @ hBOOL )
=> ( ! [F: $i] :
( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( F @ ( D @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [G: $i] :
( ( B @ ( G @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( A @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ hBOOL ) ) ) )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Relation_Ototal__on ) ) )
<=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( A @ ( D @ ( E @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( 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_total__on__def) ).
thf(2570,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( A @ ( D @ ( E @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) )
=> ( A @ ( B @ ( C @ c_Relation_Ototal__on ) ) ) )
& ( ( A @ ( B @ ( C @ c_Relation_Ototal__on ) ) )
=> ! [D: $i] :
( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( B @ ( E @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D != E )
=> ( ( A @ ( D @ ( E @ ( C @ ( C @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( C @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( 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)],[515]) ).
thf(109,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(856,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)],[109]) ).
thf(53,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(689,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)],[53]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Wellfounded_Owf ) )
=> ( ( A @ ( B @ ( D @ ( C @ ( E @ c_Recdef_Owfrec ) ) ) @ hAPP ) )
= ( A @ ( A @ ( D @ ( B @ ( D @ ( C @ ( E @ c_Recdef_Owfrec ) ) ) @ ( C @ ( E @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfrec) ).
thf(1374,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Wellfounded_Owf ) )
=> ( ( A @ ( B @ ( D @ ( C @ ( E @ c_Recdef_Owfrec ) ) ) @ hAPP ) )
= ( A @ ( A @ ( D @ ( B @ ( D @ ( C @ ( E @ c_Recdef_Owfrec ) ) ) @ ( C @ ( E @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(452,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(2253,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)],[452]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( D @ ( E @ c_Wellfounded_Owf ) )
=> ( ( A @ ( B @ ( D @ ( C @ ( E @ c_Nitpick_Owfrec_H ) ) ) ) )
= ( A @ ( E @ c_COMBI @ ( D @ ( C @ ( E @ c_Recdef_Ocut ) @ ( C @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ ( C @ ( E @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ ( E @ tc_fun ) @ ( C @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( E @ tc_fun ) @ ( C @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( C @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_COMBS ) ) @ ( C @ ( E @ tc_fun ) @ ( C @ ( E @ tc_fun ) @ ( E @ ( E @ tc_fun ) @ tc_fun ) @ ( C @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ tc_fun ) @ ( E @ ( E @ tc_fun ) @ ( C @ ( E @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( E @ c_Recdef_Owfrec__rel ) ) ) ) @ ( C @ c_HOL_OThe ) ) ) )
& ( ( D @ ( E @ c_Wellfounded_Owf ) )
=> ( ( A @ ( B @ ( D @ ( C @ ( E @ c_Nitpick_Owfrec_H ) ) ) ) )
= ( A @ ( B @ ( D @ ( C @ ( E @ c_Nitpick_Owf__wfrec_H ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Owfrec_H__def) ).
thf(2275,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( D @ ( E @ c_Wellfounded_Owf ) )
=> ( ( A @ ( B @ ( D @ ( C @ ( E @ c_Nitpick_Owfrec_H ) ) ) ) )
= ( A @ ( E @ c_COMBI @ ( D @ ( C @ ( E @ c_Recdef_Ocut ) @ ( C @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ ( C @ ( E @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( C @ ( E @ tc_fun ) @ ( C @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( C @ ( E @ tc_fun ) @ ( C @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( C @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( E @ c_COMBS ) ) @ ( C @ ( E @ tc_fun ) @ ( C @ ( E @ tc_fun ) @ ( E @ ( E @ tc_fun ) @ tc_fun ) @ ( C @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ tc_fun ) @ ( E @ ( E @ tc_fun ) @ ( C @ ( E @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( E @ c_Recdef_Owfrec__rel ) ) ) ) @ ( C @ c_HOL_OThe ) ) ) )
& ( ( D @ ( E @ c_Wellfounded_Owf ) )
=> ( ( A @ ( B @ ( D @ ( C @ ( E @ c_Nitpick_Owfrec_H ) ) ) ) )
= ( A @ ( B @ ( D @ ( C @ ( E @ c_Nitpick_Owf__wfrec_H ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oassoc) ).
thf(584,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(55,axiom,
tc_Nat_Onat @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(694,plain,
tc_Nat_Onat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(442,axiom,
( c_FunDef_Omin__strict
= ( c_FunDef_Opair__less @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Omin__ext ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__strict__def) ).
thf(2225,plain,
( c_FunDef_Omin__strict
= ( c_FunDef_Opair__less @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Omin__ext ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_FuncSet_Oextensional__funcset ) ) ) )
= ( B @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( C @ ( D @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__def) ).
thf(843,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_FuncSet_Oextensional__funcset ) ) ) )
= ( B @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( A @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( B @ ( C @ ( D @ c_FuncSet_OPi ) ) ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_fun ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( C @ ( B @ ( D @ c_Wellfounded_Olex__prod ) ) ) @ ( B @ ( D @ tc_prod ) @ c_Wellfounded_Owf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lex__prod) ).
thf(1652,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( C @ ( B @ ( D @ c_Wellfounded_Olex__prod ) ) ) @ ( B @ ( D @ tc_prod ) @ c_Wellfounded_Owf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(246,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_Otrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( 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_trancl__into__trancl2) ).
thf(1388,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_Otrancl ) @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( 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)],[246]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(579,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( B = A )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( C @ ( E @ ( F @ c_FuncSet_Oextensional ) ) @ ( A @ ( B @ ( C @ ( E @ ( D @ ( F @ c_FuncSet_Ocompose ) ) ) ) ) @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__extensional) ).
thf(1701,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( C @ ( E @ ( F @ c_FuncSet_Oextensional ) ) @ ( A @ ( B @ ( C @ ( E @ ( D @ ( F @ c_FuncSet_Ocompose ) ) ) ) ) @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb2) ).
thf(1124,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__leq @ ( D @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omax__weak @ ( C @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omax__weak @ ( C @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wmax__insertI) ).
thf(2188,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__leq @ ( D @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omax__weak @ ( C @ ( A @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omax__weak @ ( C @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(80,axiom,
c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Wellfounded_Owf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pred__nat) ).
thf(772,plain,
c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Wellfounded_Owf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(502,axiom,
( ( 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 ) @ ( v_F @ 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_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 ) @ ( v_F @ 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_bc) ).
thf(2514,plain,
( ( ( 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 ) @ ( v_F @ 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 )
=> ( 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 ) @ ( v_F @ 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____ @ ( 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 ) @ ( v_F @ 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_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 ) @ ( v_F @ 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)],[502]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downwards__aux) ).
thf(2568,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(115,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(875,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)],[115]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__greatest) ).
thf(711,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(257,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(1428,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)],[257]) ).
thf(314,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 ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__conv) ).
thf(1669,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 ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(440,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(2220,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)],[440]) ).
thf(492,axiom,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(2442,plain,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(372,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(1897,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)],[372]) ).
thf(267,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(1464,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)],[267]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_Wellfounded_Oacc ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downward) ).
thf(1638,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ c_Wellfounded_Oacc ) @ ( A @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(423,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__Int2) ).
thf(2148,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( 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 @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__subset) ).
thf(2029,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
& ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( 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 @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
thf(2326,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Product__Type_OPair ) @ ( C @ ( D @ tc_prod ) @ c_member @ ( C @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ ( C @ ( D @ tc_prod ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ c_COMBC ) ) @ ( D @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( C @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ c_COMBC ) ) @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(62,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(713,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)],[62]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__iff) ).
thf(1865,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(504,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(2521,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)],[504]) ).
thf(415,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(2119,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)],[415]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb) ).
thf(900,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(444,axiom,
c_FunDef_Opair__less @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Owf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pair__less) ).
thf(2229,plain,
c_FunDef_Opair__less @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Wellfounded_Owf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(83,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(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)],[83]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__same) ).
thf(1524,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( 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_Otrancl ) @ ( 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_Transitive__Closure_Otrancl__into__trancl) ).
thf(1349,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( 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_Otrancl ) @ ( 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)],[235]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( B @ ( A @ ( C @ c_Wellfounded_Omlex__prod ) ) @ ( C @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__mlex) ).
thf(737,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( B @ ( A @ ( C @ c_Wellfounded_Omlex__prod ) ) @ ( C @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(190,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(1122,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)],[190]) ).
thf(262,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(1439,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)],[262]) ).
thf(227,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(1307,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)],[227]) ).
thf(203,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(1175,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)],[203]) ).
thf(77,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(764,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)],[77]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ c_Relation_ODomain ) ) )
= ( A @ ( B @ ( B @ c_Relation_ODomain ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__domain) ).
thf(979,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ c_Relation_ODomain ) ) )
= ( A @ ( B @ ( B @ c_Relation_ODomain ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(26,axiom,
tc_HOL_Obool @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(604,plain,
tc_HOL_Obool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(50,axiom,
tc_Nat_Onat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(681,plain,
tc_Nat_Onat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( B @ ( C @ c_Wellfounded_Oacc ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__wfD) ).
thf(1408,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( B @ ( C @ c_Wellfounded_Oacc ) @ ( A @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( B @ ( C @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( D @ c_FuncSet_Orestrict ) ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__restrict) ).
thf(1574,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( B @ ( C @ ( D @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( D @ c_FuncSet_Orestrict ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(348,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 @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( 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_r__r__into__trancl) ).
thf(1806,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 @ ( A @ ( C @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ c_Transitive__Closure_Otrancl ) @ ( 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)],[348]) ).
thf(156,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(1011,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)],[156]) ).
thf(454,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(2257,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)],[454]) ).
thf(376,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__nat__trancl__eq__le) ).
thf(1933,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Wellfounded_Opred__nat @ ( tc_Nat_Onat @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__not__sym) ).
thf(2378,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(321,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(1690,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)],[321]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).
thf(1080,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
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(552,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(99,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(816,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)],[99]) ).
thf(414,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(2111,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)],[414]) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oless__than @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__than__iff) ).
thf(1630,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_Wellfounded_Oless__than @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Wellfounded_Oless__than @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(457,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(2267,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)],[457]) ).
thf(91,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(799,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Olattice )
=> ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(231,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 ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__conv) ).
thf(1325,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 ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(141,axiom,
v_F @ c_Arrow__Order__Mirabelle_OIIA,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I3_J) ).
thf(964,plain,
v_F @ c_Arrow__Order__Mirabelle_OIIA,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(266,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 ) )
= ( E @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__weak__cong) ).
thf(1460,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 ) )
= ( E @ ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(511,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 )
=> ( ( C @ ( A @ hAPP ) @ hBOOL )
=> ( ! [F: $i,G: $i] :
( ( B @ ( G @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( G @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( A @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ hBOOL ) ) ) )
=> ( D @ ( A @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__induct) ).
thf(2553,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 )
=> ( ( C @ ( A @ hAPP ) @ hBOOL )
=> ( ! [F: $i,G: $i] :
( ( B @ ( G @ ( F @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( G @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( G @ ( A @ hAPP ) @ hBOOL )
=> ( F @ ( A @ hAPP ) @ hBOOL ) ) ) )
=> ( D @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( B @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ ( B @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtranclp__into__rtranclp) ).
thf(1688,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( B @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ ( B @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Wellfounded_Omin__ext ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__ext__wf) ).
thf(758,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ c_Wellfounded_Omin__ext ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(525,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Relation_Oantisym ) )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisymD) ).
thf(2610,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Relation_Oantisym ) )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(494,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
<=> ! [C: $i] : ( A @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__acc__iff) ).
thf(2446,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( A @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) )
& ( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ! [C: $i] : ( A @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(621,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Opreorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(204,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(1177,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)],[204]) ).
thf(243,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(1381,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)],[243]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(685,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( C = B )
=> ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ? [E: $i] :
( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclp_Oequations_I1_J) ).
thf(1396,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ? [E: $i] :
( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ? [E: $i] :
( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
thf(959,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(214,axiom,
( ( 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_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 ) @ ( v_F @ 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',fact_ac) ).
thf(1213,plain,
( ( ( 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 ) @ ( v_F @ 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____ @ ( 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_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_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 ) @ ( v_F @ 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)],[214]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
thf(695,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Olattice )
=> ( B @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_FunDef_Opair__leq @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__leqI1) ).
thf(1643,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
=> ( c_FunDef_Opair__leq @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(608,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(395,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(2022,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)],[395]) ).
thf(506,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(2535,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)],[506]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right__if1) ).
thf(1726,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__asym) ).
thf(2401,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Wellfounded_Owf ) )
=> ( ( C @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(298,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(1594,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)],[298]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ? [E: $i] :
( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclp_Oequations_I2_J) ).
thf(2369,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ? [E: $i] :
( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ? [E: $i] :
( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) )
| ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(157,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(1015,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)],[157]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__leq @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omin__weak @ ( A @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omin__weak @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert ) ) @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wmin__insertI) ).
thf(1775,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Opair__leq @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_FunDef_Omin__weak @ ( A @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_FunDef_Omin__weak @ ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Set_Oinsert ) ) @ ( C @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_fun ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(260,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(1435,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)],[260]) ).
thf(323,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__mono) ).
thf(1694,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(126,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(922,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)],[126]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Recdef_Owfrec ) ) ) @ hAPP ) )
= ( A @ ( E @ c_COMBI @ ( C @ ( D @ ( E @ c_Recdef_Ocut ) @ ( D @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ ( D @ ( E @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ ( E @ tc_fun ) @ ( D @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( E @ tc_fun ) @ ( D @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( D @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( E @ c_COMBS ) ) @ ( D @ ( E @ tc_fun ) @ ( D @ ( E @ tc_fun ) @ ( E @ ( E @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_fun ) @ ( E @ ( E @ tc_fun ) @ ( D @ ( E @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Recdef_Owfrec__rel ) ) ) ) @ ( D @ c_HOL_OThe ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfrec__def) ).
thf(2005,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Recdef_Owfrec ) ) ) @ hAPP ) )
= ( A @ ( E @ c_COMBI @ ( C @ ( D @ ( E @ c_Recdef_Ocut ) @ ( D @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( tc_HOL_Obool @ ( E @ ( E @ tc_prod ) @ tc_fun ) @ ( D @ ( E @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ ( E @ tc_fun ) @ ( D @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ ( D @ ( E @ tc_fun ) @ ( D @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ ( D @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( E @ c_COMBS ) ) @ ( D @ ( E @ tc_fun ) @ ( D @ ( E @ tc_fun ) @ ( E @ ( E @ tc_fun ) @ tc_fun ) @ ( D @ ( E @ tc_fun ) @ ( E @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ tc_fun ) @ ( E @ ( E @ tc_fun ) @ ( D @ ( E @ tc_fun ) @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Recdef_Owfrec__rel ) ) ) ) @ ( D @ c_HOL_OThe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) )
& ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right) ).
thf(2239,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) )
& ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(409,axiom,
! [A: $i] :
( ( A @ c_Wellfounded_Omeasure )
= ( c_Wellfounded_Oless__than @ ( A @ ( tc_Nat_Onat @ c_Relation_Oinv__image ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measure__def) ).
thf(2096,plain,
! [A: $i] :
( ( A @ c_Wellfounded_Omeasure )
= ( c_Wellfounded_Oless__than @ ( A @ ( tc_Nat_Onat @ c_Relation_Oinv__image ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(226,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(1304,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)],[226]) ).
thf(340,axiom,
! [A: $i] :
( ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ~ ~ ( A @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(1758,plain,
! [A: $i] :
( ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( D @ ( C @ c_Relation_ORange ) ) @ ( B @ ( D @ ( C @ c_Relation_ORange ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ ( C @ c_Relation_ORange ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Int__subset) ).
thf(1203,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( D @ ( C @ c_Relation_ORange ) ) @ ( B @ ( D @ ( C @ c_Relation_ORange ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ ( C @ c_Relation_ORange ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le2) ).
thf(944,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( A @ ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(467,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(2318,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)],[467]) ).
thf(47,axiom,
tc_HOL_Obool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(663,plain,
tc_HOL_Obool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__commute) ).
thf(927,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C1_C) ).
thf(2503,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( B @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( c_Arrow__Order__Mirabelle_OProf @ ( A @ ( tc_HOL_Obool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ! [G: $i] :
( ( ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( G @ ( B @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( ( B @ ( v_F @ hAPP ) @ ( E @ ( F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( v_F @ hAPP ) @ ( C @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(386,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 )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = D ) ) )
=> ( A @ ( B @ c_Relation_Oantisym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisymI) ).
thf(1990,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 )
=> ( ( A @ ( C @ ( D @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = D ) ) )
=> ( A @ ( B @ c_Relation_Oantisym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclp_Otrancl__into__trancl) ).
thf(2597,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C != B )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertE) ).
thf(1181,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C != B )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ c_HOL_Oundefined ) ) )
& ( ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut__def) ).
thf(1551,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( B @ c_HOL_Oundefined ) ) )
& ( ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D2) ).
thf(1905,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( tc_HOL_Obool @ ( E @ tc_fun ) @ ( F @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(255,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(1420,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)],[255]) ).
thf(97,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(812,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)],[97]) ).
thf(277,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(1509,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)],[277]) ).
thf(464,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(2298,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)],[464]) ).
thf(280,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(1516,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)],[280]) ).
thf(114,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(872,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)],[114]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ c_Relation_ORange ) ) )
= ( A @ ( B @ ( B @ c_Relation_ORange ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__range) ).
thf(705,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ c_Relation_ORange ) ) )
= ( A @ ( B @ ( B @ c_Relation_ORange ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( F @ ( E @ ( A @ ( D @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( C @ ( E @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__cut__apply) ).
thf(1225,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ ( F @ ( E @ ( A @ ( D @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( C @ ( E @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(436,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(2192,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)],[436]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( B @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ ( B @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclp__into__tranclp2) ).
thf(2012,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( E @ ( B @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ ( B @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(517,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(2588,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)],[517]) ).
thf(481,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Oacyclic ) )
<=> ! [C: $i] :
~ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( 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_acyclic__def) ).
thf(2386,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Wellfounded_Oacyclic ) ) )
& ( ( A @ ( B @ c_Wellfounded_Oacyclic ) )
=> ! [C: $i] :
~ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( 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)],[481]) ).
thf(287,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(1547,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)],[287]) ).
thf(82,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(776,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)],[82]) ).
thf(69,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ c_Relation_Oantisym ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__Id__on) ).
thf(739,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Relation_OId__on ) @ ( B @ c_Relation_Oantisym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(503,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(2518,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)],[503]) ).
thf(271,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Wellfounded_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclicI) ).
thf(1484,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Wellfounded_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclp__into__tranclp1) ).
thf(2160,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(496,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(2454,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)],[496]) ).
thf(207,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(1188,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)],[207]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).
thf(840,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(179,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(1085,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)],[179]) ).
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(544,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(328,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(1711,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)],[328]) ).
thf(275,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(1499,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)],[275]) ).
thf(95,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(808,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)],[95]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_FunDef_Opair__leq @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__leqI2) ).
thf(2545,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( c_FunDef_Opair__leq @ ( A @ ( C @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ tc_prod ) @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(521,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(2599,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)],[521]) ).
thf(449,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Wellfounded_Omeasure @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__measure) ).
thf(2247,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Wellfounded_Omeasure @ hAPP ) @ ( B @ c_Wellfounded_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F != E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) )
& ( ( F = E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__def) ).
thf(1766,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F != E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) )
& ( ( F = E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(373,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(1898,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)],[373]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(656,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Orderings_Oorder )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( C = A )
=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(167,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(1052,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)],[167]) ).
thf(338,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_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclp__trancl__eq) ).
thf(1749,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ 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_Transitive__Closure_Otranclp ) @ 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_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__apply) ).
thf(1585,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Olattice )
=> ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oidem) ).
thf(571,plain,
! [A: $i,B: $i] :
( ( B @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( A @ ( B @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Wellfounded_Owf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__subset) ).
thf(1372,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( ( B @ ( A @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ c_Wellfounded_Owf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(196,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 )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( A @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtranclE) ).
thf(1141,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 )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( A @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
<=> ! [C: $i] :
( ? [D: $i] : ( C @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ ( D @ ( E @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( E @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( C @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).
thf(1536,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ? [D: $i] : ( C @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ ( D @ ( E @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( E @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( C @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) )
& ( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ! [C: $i] :
( ? [D: $i] : ( C @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ! [E: $i] :
( ( A @ ( D @ ( E @ ( B @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( B @ ( B @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( E @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( C @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(220,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(1272,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)],[220]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(612,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insert) ).
thf(2352,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_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( 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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).
thf(2078,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(208,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(1189,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)],[208]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( E @ ( D @ hAPP ) @ hBOOL )
=> ( E @ ( B @ hAPP ) @ ( C @ c_Wellfounded_Owf ) ) )
=> ( B @ ( D @ ( C @ ( A @ c_Recdef_Osame__fst ) ) ) @ ( C @ ( A @ tc_prod ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__same__fst) ).
thf(1390,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( E @ ( D @ hAPP ) @ hBOOL )
=> ( E @ ( B @ hAPP ) @ ( C @ c_Wellfounded_Owf ) ) )
=> ( B @ ( D @ ( C @ ( A @ c_Recdef_Osame__fst ) ) ) @ ( C @ ( A @ tc_prod ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(185,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(1108,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(1998,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( B != A )
<=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(671,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(351,axiom,
! [A: $i] :
( ( v_c____ @ ( v_a____ @ ( 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 ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ 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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_A_061_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_096) ).
thf(1817,plain,
! [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_c____ @ ( v_a____ @ ( 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 ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ 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 ) )
& ( ( v_c____ @ ( v_a____ @ ( 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 ) @ ( c_Arrow__Order__Mirabelle_Obelow @ hAPP ) @ hAPP ) @ 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(357,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( B @ c_Product__Type_OPair ) @ ( B @ ( B @ tc_prod ) @ c_member @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Wellfounded_OwfP ) )
<=> ( A @ ( B @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__wf__eq) ).
thf(1844,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( B @ c_Product__Type_OPair ) @ ( B @ ( B @ tc_prod ) @ c_member @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Wellfounded_OwfP ) ) )
& ( ( A @ ( B @ ( B @ c_Product__Type_OPair ) @ ( B @ ( B @ tc_prod ) @ c_member @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ ( B @ ( B @ tc_prod ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_COMBC ) ) @ hAPP ) @ hAPP ) @ ( B @ c_Wellfounded_OwfP ) )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(121,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(903,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)],[121]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert ) ) @ ( D @ c_Wellfounded_Oacyclic ) )
<=> ( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Wellfounded_Oacyclic ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__insert) ).
thf(1654,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Wellfounded_Oacyclic ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert ) ) @ ( D @ c_Wellfounded_Oacyclic ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_Set_Oinsert ) ) @ ( D @ c_Wellfounded_Oacyclic ) )
=> ( ~ ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( D @ c_Wellfounded_Oacyclic ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(253,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(1412,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)],[253]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( A @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclp_Or__into__trancl) ).
thf(1781,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( D @ ( A @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
<=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__inf) ).
thf(891,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
& ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(459,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(2273,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD) ).
thf(1674,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( A @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(451,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(2251,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)],[451]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( D @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(1062,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( D @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
thf(652,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Opreorder )
=> ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Ocommute) ).
thf(632,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Lattices_Osemilattice__inf )
=> ( ( A @ ( B @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( C @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).
thf(1854,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI2) ).
thf(2130,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(84,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(786,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oord )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(1276,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B ) )
=> ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(519,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(2591,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)],[519]) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(1385,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_COMBI @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( A @ ( B @ ( C @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclp_Oequations_I1_J) ).
thf(1721,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( A @ ( B @ ( C @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(461,axiom,
! [A: $i,B: $i] :
( ! [C: $i] : ( A @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__wfI) ).
thf(2283,plain,
! [A: $i,B: $i] :
( ! [C: $i] : ( A @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) )
& ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left) ).
thf(1476,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) )
& ( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Set_Oinsert ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(135,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(946,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)],[135]) ).
thf(182,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(1101,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)],[182]) ).
thf(363,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(1861,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)],[363]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Orefl__on ) ) )
=> ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD1) ).
thf(1777,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Orefl__on ) ) )
=> ( ( C @ ( A @ ( B @ ( E @ ( E @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( E @ ( E @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(224,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(1294,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)],[224]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclp__rtranclp__tranclp) ).
thf(2198,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ ( E @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( B @ c_HOL_Oundefined ) ) )
& ( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__def) ).
thf(2162,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ~ ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( B @ c_HOL_Oundefined ) ) )
& ( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ ( E @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(279,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 ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Osimps_I2_J) ).
thf(1513,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 ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Wellfounded_Oacc ) @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
thf(1661,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ c_Wellfounded_Oacc ) @ ( B @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ c_Wellfounded_Oacc ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(264,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(1444,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)],[264]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( B @ c_FunDef_Oin__rel ) ) @ ( B @ c_Wellfounded_OwfP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__in__rel) ).
thf(1045,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( B @ c_FunDef_Oin__rel ) ) @ ( B @ c_Wellfounded_OwfP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(445,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
thf(2230,plain,
v_a____ != v_b____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(399,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_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclp__rtrancl__eq) ).
thf(2036,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ 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_Transitive__Closure_Ortranclp ) @ 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_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( A @ ( B @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(151,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 ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__curry) ).
thf(999,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 ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( B @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).
thf(1678,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( B @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_FunDef_Oreduction__pair ) )
=> ( A @ ( C @ ( B @ ( D @ c_FunDef_Orp__inv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_FunDef_Oreduction__pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
thf(2255,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_FunDef_Oreduction__pair ) )
=> ( A @ ( C @ ( B @ ( D @ c_FunDef_Orp__inv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_FunDef_Oreduction__pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(181,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(1097,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)],[181]) ).
thf(446,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(2233,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)],[446]) ).
thf(301,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(1625,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)],[301]) ).
thf(523,axiom,
! [A: $i,B: $i] :
( ( c_fequal @ ( c_fNot @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ c_Transitive__Closure_Ortranclp ) )
= ( A @ ( B @ c_Transitive__Closure_Ortranclp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclp__r__diff__Id) ).
thf(2604,plain,
! [A: $i,B: $i] :
( ( c_fequal @ ( c_fNot @ ( B @ ( tc_HOL_Obool @ ( tc_HOL_Obool @ c_COMBB ) ) @ hAPP ) @ ( B @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( A @ ( tc_HOL_Obool @ ( B @ tc_fun ) @ ( B @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ c_Transitive__Closure_Ortranclp ) )
= ( A @ ( B @ c_Transitive__Closure_Ortranclp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(368,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_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C != B ) )
| ( C = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclD) ).
thf(1876,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_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C != B ) )
| ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_Oextensional__funcset ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_extensional__funcset__mem) ).
thf(1527,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_Oextensional__funcset ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI1) ).
thf(790,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
=> ( B @ ( A @ ( C @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI2) ).
thf(867,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Lattices_Osemilattice__inf )
=> ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( C @ ( A @ ( D @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(67,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(735,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)],[67]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( D @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1I) ).
thf(2003,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ( C @ ( B @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( D @ ( tc_HOL_Obool @ ( A @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Oacyclic ) )
=> ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Relation_Oantisym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).
thf(1116,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_Oacyclic ) )
=> ( A @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( B @ c_Relation_Oantisym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(375,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(1908,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)],[375]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( D @ ( E @ ( G @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( G @ ( B @ ( D @ ( C @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( A @ ( B @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( D @ ( C @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfrec__rel_Ointros) ).
thf(2008,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( D @ ( E @ ( G @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( G @ ( A @ hAPP ) @ ( G @ ( B @ ( D @ ( C @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL ) )
=> ( E @ ( A @ ( B @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( D @ ( C @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(384,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(1986,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)],[384]) ).
thf(362,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(1859,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)],[362]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__Int1) ).
thf(2334,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_Owf ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(476,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(2366,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)],[476]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( E @ hAPP ) )
= C )
=> ( ( C @ ( D @ ( E @ ( A @ ( B @ c_Fun_Ofun__upd ) ) ) ) )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
thf(1197,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( D @ ( E @ hAPP ) )
= C )
=> ( ( C @ ( D @ ( E @ ( A @ ( B @ c_Fun_Ofun__upd ) ) ) ) )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(407,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut__apply) ).
thf(2091,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( E @ ( D @ ( C @ ( A @ ( B @ ( F @ c_Recdef_Ocut ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclE) ).
thf(1891,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( E @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( E @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(102,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(828,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)],[102]) ).
thf(172,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(1065,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)],[172]) ).
thf(89,axiom,
c_Wellfounded_Oless__than @ ( tc_Nat_Onat @ c_Wellfounded_Owf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__less__than) ).
thf(796,plain,
c_Wellfounded_Oless__than @ ( tc_Nat_Onat @ c_Wellfounded_Owf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(124,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(918,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)],[124]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Osingle__valued ) ) )
=> ( ( A @ ( B @ ( D @ c_Relation_Osingle__valued ) ) )
=> ( A @ ( C @ ( B @ ( D @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( B @ ( E @ c_Relation_Osingle__valued ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__rel__comp) ).
thf(801,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Relation_Osingle__valued ) ) )
=> ( ( A @ ( B @ ( D @ c_Relation_Osingle__valued ) ) )
=> ( A @ ( C @ ( B @ ( D @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( B @ ( E @ c_Relation_Osingle__valued ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) ) @ ( B @ ( C @ ( D @ c_Product__Type_Ocurry ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__split) ).
thf(897,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Product__Type_Oprod_Oprod__case ) ) ) @ ( B @ ( C @ ( D @ c_Product__Type_Ocurry ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(252,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(1410,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)],[252]) ).
thf(78,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(767,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)],[78]) ).
thf(168,axiom,
v_F @ c_Arrow__Order__Mirabelle_Ounanimity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_u) ).
thf(1056,plain,
v_F @ c_Arrow__Order__Mirabelle_Ounanimity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(664,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( ( A = B )
=> ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclp__into__rtranclp) ).
thf(2223,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(635,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Oorder )
=> ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Osemilattice__inf )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__mono) ).
thf(728,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ class_Lattices_Osemilattice__inf )
=> ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( C @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( B @ ( D @ ( E @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(418,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
thf(2127,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( C @ ( A @ ( B @ ( F @ ( D @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_FuncSet_Orestrict ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compose__def) ).
thf(1829,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( C @ ( A @ ( B @ ( F @ ( D @ ( E @ c_COMBB ) ) @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_FuncSet_Orestrict ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
<=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(596,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Olinorder )
=> ( ( ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
=> ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
& ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( ( B = A )
| ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__mono) ).
thf(723,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(100,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(822,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)],[100]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb2) ).
thf(850,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL )
<=> ? [G: $i] :
( ! [H: $i] :
( ( D @ ( B @ ( H @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( H @ ( G @ hAPP ) @ ( H @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL ) )
& ( A
= ( B @ ( G @ ( C @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfrec__rel_Osimps) ).
thf(2484,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ! [H: $i] :
( ( D @ ( B @ ( H @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( H @ ( G @ hAPP ) @ ( H @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL ) )
& ( A
= ( B @ ( G @ ( C @ hAPP ) @ hAPP ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL )
=> ? [G: $i] :
( ! [H: $i] :
( ( D @ ( B @ ( H @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( H @ ( G @ hAPP ) @ ( H @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL ) )
& ( A
= ( B @ ( G @ ( C @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(458,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__other) ).
thf(2270,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( F @ ( A @ ( E @ ( B @ ( C @ ( D @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( A @ ( B @ ( C @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclp_Ortrancl__refl) ).
thf(2138,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( A @ ( B @ ( C @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( D @ ( B @ ( C @ ( E @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_restrict__in__funcset) ).
thf(1532,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( D @ ( F @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( E @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_COMBK ) ) @ ( D @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( D @ ( B @ ( C @ ( E @ c_FuncSet_Orestrict ) ) ) @ ( C @ ( E @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower2) ).
thf(860,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(295,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(1582,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)],[295]) ).
thf(456,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(2265,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)],[456]) ).
thf(123,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(908,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)],[123]) ).
thf(148,axiom,
( c_FunDef_Opair__less
= ( c_Wellfounded_Oless__than @ ( c_Wellfounded_Oless__than @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Wellfounded_Olex__prod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__less__def) ).
thf(992,plain,
( c_FunDef_Opair__less
= ( c_Wellfounded_Oless__than @ ( c_Wellfounded_Oless__than @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Wellfounded_Olex__prod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( A @ ( F @ ( B @ ( G @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) )
= ( B @ ( G @ ( A @ ( F @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__twist) ).
thf(982,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( A @ ( F @ ( B @ ( G @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) )
= ( B @ ( G @ ( A @ ( F @ ( C @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( D @ ( E @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(153,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(1004,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)],[153]) ).
thf(233,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(1331,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)],[233]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).
thf(803,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Transitive__Closure_Otrancl ) @ ( B @ c_Transitive__Closure_Ortrancl ) )
= ( A @ ( B @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL )
<=> ? [G: $i] :
( ! [H: $i] :
( ( D @ ( B @ ( H @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( H @ ( G @ hAPP ) @ ( H @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= ( B @ ( G @ ( C @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfrec__rel_Oequations) ).
thf(1962,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ! [H: $i] :
( ( D @ ( B @ ( H @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( H @ ( G @ hAPP ) @ ( H @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= ( B @ ( G @ ( C @ hAPP ) @ hAPP ) ) ) )
=> ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL )
=> ? [G: $i] :
( ! [H: $i] :
( ( D @ ( B @ ( H @ ( F @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( F @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( H @ ( G @ hAPP ) @ ( H @ ( C @ ( D @ ( E @ ( F @ c_Recdef_Owfrec__rel ) ) ) ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= ( B @ ( G @ ( C @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(206,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(1184,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)],[206]) ).
thf(290,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(1565,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)],[290]) ).
thf(491,axiom,
! [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',fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096) ).
thf(2436,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)],[491]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(639,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(72,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(755,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right__if0) ).
thf(2170,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclp__trans) ).
thf(2087,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ ( E @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(592,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Oorder )
=> ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__commute) ).
thf(1069,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( B @ ( A @ ( tc_HOL_Obool @ ( C @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__assoc) ).
thf(708,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) )
= ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(379,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(1944,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)],[379]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mem) ).
thf(1367,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( F @ c_FuncSet_OPi ) ) ) @ ( D @ ( E @ ( F @ tc_fun ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(133,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(940,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)],[133]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greatest) ).
thf(935,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( ( A @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
=> ( A @ ( B @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Lattices_Osemilattice__inf__class_Oinf ) ) @ ( C @ ( tc_HOL_Obool @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(155,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(1009,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)],[155]) ).
thf(439,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_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C != B ) )
| ( C = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
thf(2206,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( A @ ( D @ c_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C != B ) )
| ( C = B ) )
=> ( 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_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_Transitive__Closure_Otrancl ) @ ( B @ ( C @ ( D @ ( D @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( D @ ( D @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
& ( C != B ) )
| ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ ( C @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( G @ ( H @ c_Relation_Orel__comp ) ) ) ) @ ( B @ ( F @ ( C @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__compI) ).
thf(1737,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( D @ ( E @ ( F @ ( G @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( G @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( E @ ( C @ ( G @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( G @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( G @ ( H @ c_Relation_Orel__comp ) ) ) ) @ ( B @ ( F @ ( C @ ( H @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( H @ tc_prod ) @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( B != A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclpD) ).
thf(1490,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Ortranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( C @ ( D @ c_Transitive__Closure_Otranclp ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( B != A ) )
| ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(163,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(1037,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)],[163]) ).
thf(4656,plain,
$false,
inference(e,[status(thm)],[645,1322,2452,1337,2094,760,2263,1559,1729,628,1840,1850,2559,555,1295,1686,1369,1823,2336,2109,1454,2412,846,1083,962,977,1596,730,1522,2381,1808,994,2590,741,2014,1205,2099,2380,1437,1158,582,762,1422,1939,614,1692,1078,2607,533,550,1735,1872,814,1988,1640,2042,1497,1705,797,2316,1507,930,2360,1095,1746,1127,2227,1441,1645,1529,1703,1228,2173,565,1430,1760,587,2562,1832,2356,2444,1264,1511,702,2185,1577,1059,1132,2420,853,2403,1147,969,770,1568,2024,2533,924,1946,1664,2105,2122,937,2324,2027,2236,623,1383,1020,574,1960,806,1169,1377,956,1072,1394,1351,660,1433,1405,877,692,2190,1943,1201,2392,2154,1696,2586,1863,920,2473,546,810,1470,1783,1636,1153,761,1311,2296,2083,2496,1047,1057,1274,1723,2601,825,2249,1580,862,1217,1666,1487,1883,952,2541,788,1619,2150,2132,2414,566,2179,682,1106,625,2433,2200,830,2313,1128,2547,2344,578,697,2157,1017,1328,1111,1672,1006,869,1755,1118,650,948,1856,725,2460,1028,1361,933,1075,637,1810,2108,554,753,1739,537,2080,642,1414,526,2551,2085,1207,590,1155,547,1744,1150,654,1974,1050,1874,569,2140,605,1825,2285,1114,647,997,2125,1588,985,1002,1852,1318,792,1779,541,1466,1286,1035,2408,1663,2089,1026,1895,773,794,1996,2423,888,906,1135,2001,965,2176,1680,1103,1219,2570,856,689,1374,2253,2275,584,694,2225,843,1652,1388,579,1701,1124,2188,772,2514,2568,875,711,1428,1669,2220,2442,1897,1464,1638,2148,2029,2326,713,1865,2521,2119,900,2229,784,1524,1349,737,1122,1439,1307,1175,764,979,604,681,1408,1574,1806,1011,2257,1933,2378,1690,1080,552,816,2111,1630,2267,799,1325,964,1460,2553,1688,758,2610,2446,621,1177,1381,685,1396,959,1213,695,1643,608,2022,2535,1726,2401,1594,2369,1015,1775,1435,1694,922,2005,2239,2096,1304,1758,1203,944,2318,663,927,2503,1990,2597,1181,1551,1905,1420,812,1509,2298,1516,872,705,1225,2192,2012,2588,2386,1547,776,739,2518,1484,2160,2454,1188,840,1085,544,1711,1499,808,2545,2599,2247,1766,1898,656,1052,1749,1585,571,1372,1141,1536,1272,612,2352,2078,1189,1390,1108,1998,671,1817,1844,903,1654,1412,1781,891,2273,1674,2251,1062,652,632,1854,2130,786,1276,2591,1385,1721,2283,1476,946,1101,1861,1777,1294,2198,2162,1513,1661,1444,1045,2230,2036,999,1678,2255,1097,2233,1625,2604,1876,1527,790,867,735,2003,1116,1908,2008,1986,1859,2334,2366,1197,2091,1891,828,1065,796,918,801,897,1410,767,1056,664,2223,635,728,2127,1829,596,723,822,850,2484,2270,2138,1532,860,1582,2265,908,992,982,1004,1331,803,1962,1184,1565,2436,639,755,2170,2087,592,1069,708,1944,1367,940,935,1009,2206,1737,1490,1037]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT147+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
% 0.12/0.39 % Computer : n003.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sat Sep 26 06:34:53 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 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
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.31/1.44 % [INFO] Parsing done (445ms).
% 2.31/1.46 % [INFO] Running in sequential loop mode.
% 3.37/1.84 % [INFO] eprover registered as external prover.
% 3.37/1.85 % [INFO] Scanning for conjecture ...
% 4.09/2.11 % [INFO] Found a conjecture (or negated_conjecture) and 523 axioms. Running axiom selection ...
% 5.77/2.44 % [INFO] Axiom selection finished. Selected 523 axioms (removed 0 axioms).
% 7.63/2.95 % [INFO] Problem is first-order (TPTP FOF).
% 7.63/2.99 % [INFO] Type checking passed.
% 7.63/3.00 % [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 ...
% 60.86/28.82 % External prover 'e' found a proof!
% 60.86/28.82 % [INFO] Killing All external provers ...
% 60.86/28.82 % Time passed: 28281ms (effective reasoning time: 27359ms)
% 60.86/28.82 % 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)>
% 60.86/28.83 % Axioms used in derivation (523): fact_wf__not__refl, fact_wmax__insertI, fact_xt1_I1_J, fact_converse__rtrancl__induct2, fact_single__valued__Id__on, fact_insertCI, arity_fun__Orderings_Oorder, fact_wf__not__sym, fact_wf__inv__image, fact_wfrec__def, fact_tranclp__into__rtranclp, fact_acc__wfI, fact_order__le__neq__trans, fact_Int__insert__left__if1, fact_adm__wf__def, fact_Pi__I, fact_rtranclpD, fact_wfrec__rel_Ointros, fact_refl__onD2, fact_Int__lower1, fact_cut__apply, fact_le__inf__iff, fact_accp_Oequations, fact_inf2I, fact_order__le__less__trans, fact_smax__insertI, fact_insert__iff, fact__C1_C, arity_Nat__Onat__Lattices_Olattice, fact_le__eq__less__or__eq, fact_nat__less__cases, fact_IIA__def, fact_xt1_I4_J, fact_cut__def, fact_unanimity__def, fact_compose__Id, fact__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096, fact_Range__Int__subset, fact_inf__sup__aci_I4_J, fact_inf_Oassoc, fact_pair__lessI2, fact_termination__basic__simps_I5_J, fact_insert__subset, fact_restrictI, fact_curry__split, fact_rtranclD, fact_less__imp__le__nat, fact_pred__nat__trancl__eq__le, fact_Transitive__Closure_Otrancl__into__trancl, fact_prod_Orecs, fact_curry__conv, fact_insertI1, fact_order__less__asym_H, arity_Nat__Onat__Orderings_Oorder, fact_curry__def, fact_O__assoc, fact_wmin__insertI, fact_min__ext__wf, fact_linorder__not__le, fact_order__eq__refl, fact_Pi__I_H, fact_Id__compose, fact_in__mktop, fact_inf__absorb1, arity_HOL__Obool__Orderings_Opreorder, fact_extensionalityI, fact_in__mkbot, fact_linorder__neqE, fact_curryE, fact_leI, fact_Int__left__commute, fact_assms_I1_J, help_c__fconj__3, 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_r__into__trancl_H, fact_rel__compI, fact_pred__equals__eq2, help_c__COMBC__1, fact_inf__sup__ord_I2_J, help_c__fequal__2, fact_wf__Int1, fact_acyclic__impl__antisym__rtrancl, fact_le__neq__implies__less, fact_tranclD2, fact_below__Lin, fact_converse__rtrancl__induct, help_c__fFalse__1, fact_linorder__antisym__conv3, fact_order__less__imp__not__eq, fact_rtranclp__tranclp__tranclp, fact_min__strict__def, fact_max__rpair__set, fact_rtranclp_Oequations_I1_J, fact_rtrancl__mono, fact_rtrancl__subset__rtrancl, fact_prod_Osimps_I2_J, fact_converse__rtranclE2, fact_Int__insert__right, fact_split__paired__All, fact_complete__Lin, fact_less__eq, fact_rp__inv__image__def, fact_inf__fun__def, fact_acc_OaccI, fact_equalityD2, fact_extensional__funcset__def, fact_less__infI2, fact_linorder__antisym__conv1, fact_tranclE, fact_inf1D2, fact_antisymI, fact_inf_Oleft__commute, fact_predicate2D, fact_single__valued__rel__comp, fact_le__funD, fact_reduction__pairI, fact_Pi__mem, fact_inf2D1, fact_le__fun__def, fact_acc__subset, fact_wf__measure, fact_extensional__funcset__mem, help_c__COMBS__1, fact_split__twice, fact_wf__irrefl, fact_override__on__def, fact_order__less__imp__not__less, fact_fun__upd__same, arity_fun__Lattices_Osemilattice__inf, fact_inf__Int__eq, fact_extensional__funcset__arb, fact_ord__less__eq__trans, fact_in__mono, fact_wf__lex__prod, fact_Int__absorb2, fact_r__comp__rtrancl__eq, fact_xt1_I9_J, help_c__COMBI__1, fact_linorder__less__linear, fact_rtranclp__trans, fact_rtranclp__into__tranclp2, fact_mkbot__Lin, fact_Int__assoc, fact_in__measure, fact_funcset__mem, fact_rtrancl__subset, fact_subset__iff__psubset__eq, fact_single__valued__subset, fact_Id__on__iff, fact_less__or__eq__imp__le, arity_HOL__Obool__Lattices_Olattice, fact_wf__subset, fact_inf__commute, help_c__fconj__2, arity_Nat__Onat__Orderings_Opreorder, fact_refl__onD, fact_fun__upd__idem, fact_order__less__imp__not__eq2, fact_tfl__cut__apply, fact_accp__downwards, fact_Int__insert__left, fact_Domain__insert, fact_order__antisym, fact_xt1_I10_J, fact_less__irrefl__nat, fact_order__refl, fact_acc__downwards, fact_Int__insert__right__if0, fact_dictator__def, fact_wfP__trancl, fact_inf1I, fact_inf_Oidem, fact_Domain__mono, fact_wf__Int2, help_c__fNot__1, fact_tranclp_Oequations_I1_J, fact_xt1_I5_J, fact_insert__code, fact_inf2E, fact_fun__upd__other, fact_adm__lemma, fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096, fact_le__infI2, fact_nat__neq__iff, fact_RangeI, fact_extensional__funcset__extend__domainI, fact_compose__extensional, fact_DomainI, fact__C2_C, fact_inf__sup__ord_I1_J, fact_inf1E, fact_Pi__cong, fact_inf__left__commute, fact_eq__mem, fact_inf__left__idem, fact_subset__insertI, fact_xt1_I3_J, fact_wf__pred__nat, fact_less__imp__neq, fact_xt1_I8_J, fact_predicate1D, fact_less__not__refl3, fact_wfP__empty, fact_notin__Lin__iff, fact_accp__subset, fact_smin__insertI, arity_HOL__Obool__Orderings_Oord, fact__096a_A_126_061_Ab_096, fact_Id__onE, fact_RangeE, fact_insertI2, fact_compose__assoc, fact_insert__absorb, fact_subset__insert, fact_insert__absorb2, fact_rtranclp__into__tranclp1, fact_fun__upd__apply, fact_converse__rtranclE, fact_less__infI1, fact__096P_H_A_058_AProf_096, fact_eqset__imp__iff, fact_same__fstI, fact_order__neq__le__trans, fact_trancl__trans, fact_equalityD1, fact_converse__rtrancl__into__rtrancl, fact_wfP__accp__iff, fact_inf2D2, fact_le__funE, fact_extensional__arb, fact_wfrec, fact_Nitpick_Owfrec_H__def, fact_rtranclp_Ortrancl__into__rtrancl, arity_Nat__Onat__Orderings_Oord, arity_fun__Orderings_Opreorder, fact_rtrancl__trans, fact_accp__wfPD, fact_irrefl__def, fact_extensional__funcset__restrict__domain, fact_override__on__apply__in, fact_extensional__restrict, help_c__fequal__1, fact_in__above, fact_insert__inter__insert, fact_linorder__neq__iff, fact_mlex__leq, fact_rp__inv__image__rp, fact_Int__lower2, fact_insert__commute, fact_fun__upd__triv, fact_DomainP__Domain__eq, fact_in__below, fact_Int__absorb, fact_ord__le__eq__trans, fact_antisym__subset, fact_le__infE, fact_set__mp, fact_less__than__iff, fact_DomainP_Ointros, fact_total__on__def, fact_accp__downward, fact_not__less__iff__gr__or__eq, fact_mktop__Lin, fact_irrefl__trancl__rD, fact_fun__upd__idem__iff, fact_ab, fact_wfrec__rel_Oequations, fact_def__wfrec, fact_Range__Id__on, fact_funcset__compose, fact_tranclp__into__tranclp2, fact_bc, fact_linorder__neqE__nat, fact_psubsetD, fact_le__iff__inf, fact_r__r__into__trancl, fact_wfrec__unique, fact_inf_Ocommute, fact_antisym__def, fact_wf__acc__iff, fact_tranclp__trancl__eq, fact_set__eq__subset, fact_rtrancl__into__trancl2, fact_acyclic__insert, fact_Nitpick_Orefl_H__def, fact_psubset__trans, fact_pred__subset__eq, fact_iff, fact_order__less__le, fact_inf__greatest, fact_Range__iff, help_c__fconj__1, fact_Pair__inject, fact_xt1_I12_J, fact_subset__refl, fact__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_A_061_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_096, fact_inf__le1, help_c__fNot__2, fact_inf1D1, fact_acc__wfD, fact_RangeP_Ointros, fact_inf__Int__eq2, fact_internal__split__conv, arity_fun__Orderings_Oord, fact_equalityI, fact_ext, fact_order__less__not__sym, arity_HOL__Obool__Orderings_Oorder, fact_linorder__le__less__linear, fact_single__valued__confluent, fact_le__infI, fact_wf__in__rel, fact_less__le__not__le, arity_Nat__Onat__Orderings_Olinorder, fact_RangeP__Range__eq, fact_nat__le__linear, fact_linorder__le__cases, fact_inf__apply, fact_split__eta, fact_assms_I3_J, fact_Id__on__eqI, fact_acyclic__def, fact_order__less__le__trans, fact_fun__upd__upd, fact_Int__commute, fact_PiE, fact_rtrancl__induct2, fact_rtrancl__trancl__absorb, fact_compose__def, fact_inf__mono, fact_trancl__range, fact_trancl__into__rtrancl, 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_converse__tranclE, fact_refl__onD1, fact_not__leE, fact_leD, fact_insert__ident, fact__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096, fact_wf__eq__minimal, fact_acyclic__subset, fact_wf__comp__self, fact_curryD, fact_less__than__def, fact_IntD2, fact_rtrancl__eq__or__trancl, help_c__COMBB__1, fact_extensional__subset, fact_order__less__asym, fact_the__inv__into__def, fact_override__on__apply__notin, fact_mlex__less, fact_psubset__imp__subset, fact_trancl_Or__into__trancl, fact_min__rpair__set, fact_funcset__id, fact_set__rev__mp, fact_tranclD, fact_Domain__iff, fact_inf__absorb2, fact_pair__less__def, fact_eq__mem__trans, fact_Int__mono, fact_antisymD, fact_acc__downwards__aux, fact_wf__insert, fact_rtrancl__induct, fact_mlex__prod__def, fact_RangeP_Oequations, fact_rev__predicate2D, fact_linorder__linear, fact_trancl__into__trancl2, fact_single__valuedI, fact_le__refl, fact_subset__insertI2, fact_Int__insert__right__if1, fact_less__not__refl2, fact_rtranclp__mono, fact_the__sym__eq__trivial, fact_trancl__rtrancl__absorb, arity_HOL__Obool__Lattices_Osemilattice__inf, fact_DomainE, fact_xt1_I6_J, fact_Domain__Int__subset, fact_tranclp_Otrancl__into__trancl, fact_single__valued__def, fact_accp_Osimps, fact_tranclp_Or__into__trancl, fact_tranclp__trans, fact_linorder__not__less, fact_Int__absorb1, fact_restrict__apply, fact_inf__sup__aci_I3_J, fact_refl__on__Int, fact_xt1_I2_J, fact_less__fun__def, fact_rev__predicate1D, fact_in__lex__prod, fact_rtranclp__subset, fact_Domain__Id__on, fact_cuts__eq, fact_trancl__unfold__right, fact_inf_Oleft__idem, fact__096P_A_058_AProf_096, fact_wf__trancl, fact_pair__leqI1, fact_converse__rtranclp__into__rtranclp, fact_tfl__wfrec, fact_in__rel__def, fact_subset__psubset__trans, fact_accp__acc__eq, fact_order__eq__iff, fact_equalityE, fact_split__curry, fact_Pair__eq, fact_restrict__in__funcset, fact_inf__assoc, fact_rtrancl_Ortrancl__into__rtrancl, fact_rtranclE, fact_Lin__irrefl, fact_Int__insert__left__if0, fact_split__conv, fact_measure__def, fact_split__weak__cong, fact_less__not__refl, fact_insert__mono, fact_ord__eq__less__trans, fact_fun__upd__def, fact_le__trans, fact_inf__le2, fact_wf__mlex, fact_accp__downwards__aux, fact_fun__upd__twist, fact_equalityCE, fact_r__into__rtrancl, help_c__COMBK__1, fact_Nitpick_Owf__wfrec_H__def, fact_restrict__def, fact_rtrancl__into__trancl1, fact_Not__Domain__rtrancl, fact_rtrancl__idemp, fact_IntI, fact_subsetD, fact_tranclp__rtranclp__tranclp, fact_psubset__eq, fact_funcsetI, fact_trancl__rtrancl__trancl, fact_u, fact_wf__same__fst, fact_above__Lin, fact_dictatorI, fact_eq__imp__le, fact_trancl__unfold__left, fact_Range__insert, fact_in__inv__image, fact_insertE, fact_acyclicI, fact_acc__downward, fact_r__into__rtranclp, fact_tranclp_Oequations_I2_J, fact_order__le__imp__less__or__eq, fact_curryI, fact_order__antisym__conv, fact_wf__acyclic, fact_le__antisym, fact_eqelem__imp__iff, fact_pred__equals__eq, fact_Int__greatest, fact_psubset__subset__trans, fact_rtranclp_Oequations_I2_J, fact_antisym__Id__on, fact_subset__trans, fact_IntE, fact_inf__sup__aci_I2_J, fact_the__eq__trivial, fact_wfP__wf__eq, fact_pair__lessI1, fact_order__less__trans, fact_wf__asym, fact_rtrancl__idemp__self__comp, fact_le__infI1, fact_pair__leqI2, fact_IntD1, fact__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_058_AProf_096, fact_compose__eq, fact_order__less__irrefl, fact_rtranclp__rtrancl__eq, fact_Int__iff, fact_order__le__less, fact_rtranclp__idemp, fact_Int__left__absorb, fact_order__less__imp__le, fact_mem__def, fact_refl__on__Id__on, fact_nat__less__le, fact_wf__pair__less, fact_trancl__mono, fact_ord__eq__le__trans, fact_wf__less__than, fact_inf__sup__aci_I1_J, fact_wfrec__rel_Osimps, fact_pred__subset__eq2, fact_inf__idem, fact_linorder__cases, fact_xt1_I11_J, fact_wfP__subset, fact_rtrancl__trancl__trancl, fact_not__acc__down, fact__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096, fact_xt1_I7_J, fact_order__trans, fact_ac, fact_rtranclp__r__diff__Id, fact_rtranclp_Ortrancl__refl, fact_single__valuedD, fact_const__Lin__Prof, fact_restrict__extensional, fact_trancl__domain
% 60.86/28.83 % No. of inferences in proof: 1050
% 60.86/28.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 28281 ms resp. 27359 ms w/o parsing
% 63.17/29.42 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 63.17/29.42 % [INFO] Killing All external provers ...
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