TSTP Solution File: SCT105+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT105+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:50:34 EDT 2023
% Result : Theorem 17.87s 5.09s
% Output : Refutation 18.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 603
% Syntax : Number of formulae : 1125 ( 265 unt; 83 typ; 0 def)
% Number of atoms : 2904 ( 590 equ; 0 cnn)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 19229 ( 294 ~; 79 |; 247 &;17073 @)
% ( 101 <=>;1435 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 185 ( 185 >; 0 *; 0 +; 0 <<)
% Number of symbols : 85 ( 83 usr; 14 con; 0-6 aty)
% Number of variables : 3587 ( 0 ^;3541 !; 46 ?;3587 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Relation_Otrans_type,type,
c_Relation_Otrans: $i > $i > $o ).
thf(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(v_L_type,type,
v_L: $i ).
thf(c_member_type,type,
c_member: $i > $i > $i > $o ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i > $i > $i ).
thf(class_Lattices_Osemilattice__sup_type,type,
class_Lattices_Osemilattice__sup: $i > $o ).
thf(c_Lattices_Osemilattice__sup__class_Osup_type,type,
c_Lattices_Osemilattice__sup__class_Osup: $i > $i > $i > $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Groups_Ominus_type,type,
class_Groups_Ominus: $i > $o ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(class_Lattices_Obounded__lattice__bot_type,type,
class_Lattices_Obounded__lattice__bot: $i > $o ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_Relation_OId_type,type,
c_Relation_OId: $i > $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i > $i ).
thf(c_Relation_ORange_type,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Wellfounded_Owf_type,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(c_Wellfounded_Omlex__prod_type,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(c_Relation_Oantisym_type,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(c_Relation_OId__on_type,type,
c_Relation_OId__on: $i > $i > $i ).
thf(c_Wellfounded_Omin__ext_type,type,
c_Wellfounded_Omin__ext: $i > $i > $i ).
thf(c_Wellfounded_Omeasure_type,type,
c_Wellfounded_Omeasure: $i > $i ).
thf(c_Relation_Oinv__image_type,type,
c_Relation_Oinv__image: $i > $i > $i > $i ).
thf(c_Wellfounded_Oless__than_type,type,
c_Wellfounded_Oless__than: $i ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Set_Othe__elem_type,type,
c_Set_Othe__elem: $i > $i > $i ).
thf(c_Wellfounded_Opred__nat_type,type,
c_Wellfounded_Opred__nat: $i ).
thf(c_Nitpick_Ofold__graph_H_type,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Relation_Osingle__valued_type,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(c_Recdef_Owfrec_type,type,
c_Recdef_Owfrec: $i > $i > $i > $i > $i ).
thf(c_Recdef_Ocut_type,type,
c_Recdef_Ocut: $i > $i > $i > $i > $i > $i ).
thf(c_Wellfounded_Oacyclic_type,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(c_Order__Relation_Opartial__order__on_type,type,
c_Order__Relation_Opartial__order__on: $i > $i > $i > $o ).
thf(c_Order__Relation_Opreorder__on_type,type,
c_Order__Relation_Opreorder__on: $i > $i > $i > $o ).
thf(class_Groups_Oordered__ab__group__add_type,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
thf(class_Groups_Oab__group__add_type,type,
class_Groups_Oab__group__add: $i > $o ).
thf(c_Relation_Ototal__on_type,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(c_Relation_OField_type,type,
c_Relation_OField: $i > $i > $i ).
thf(c_Wellfounded_Omax__ext_type,type,
c_Wellfounded_Omax__ext: $i > $i > $i ).
thf(c_Nitpick_Owf__wfrec_H_type,type,
c_Nitpick_Owf__wfrec_H: $i > $i > $i > $i > $i > $i ).
thf(c_Nitpick_Owf__wfrec_type,type,
c_Nitpick_Owf__wfrec: $i > $i > $i > $i > $i ).
thf(c_FunDef_Opair__less_type,type,
c_FunDef_Opair__less: $i ).
thf(c_Wellfounded_Olex__prod_type,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_FunDef_Oreduction__pair_type,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(c_FunDef_Orp__inv__image_type,type,
c_FunDef_Orp__inv__image: $i > $i > $i > $i > $i ).
thf(c_Wellfounded_OwfP_type,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(c_FunDef_Oin__rel_type,type,
c_FunDef_Oin__rel: $i > $i > $i > $i ).
thf(c_Order__Relation_Olinear__order__on_type,type,
c_Order__Relation_Olinear__order__on: $i > $i > $i > $o ).
thf(c_Relation_Orefl__on_type,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(c_Recdef_Osame__fst_type,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oequiv_type,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(c_Relation_Orel__comp_type,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Relation_Oirrefl_type,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(c_Recdef_Owfrec__rel_type,type,
c_Recdef_Owfrec__rel: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Wellfounded_Oacc_type,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(c_FunDef_Opair__leq_type,type,
c_FunDef_Opair__leq: $i ).
thf(c_Product__Type_Ocurry_type,type,
c_Product__Type_Ocurry: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Order__Relation_Owell__order__on_type,type,
c_Order__Relation_Owell__order__on: $i > $i > $i > $o ).
thf(c_Product__Type_Oprod_Oprod__rec_type,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(c_FunDef_Omin__weak_type,type,
c_FunDef_Omin__weak: $i ).
thf(c_FunDef_Omax__weak_type,type,
c_FunDef_Omax__weak: $i ).
thf(c_FunDef_Omax__strict_type,type,
c_FunDef_Omax__strict: $i ).
thf(c_FunDef_Omin__strict_type,type,
c_FunDef_Omin__strict: $i ).
thf(c_Order__Relation_Ostrict__linear__order__on_type,type,
c_Order__Relation_Ostrict__linear__order__on: $i > $i > $i > $o ).
thf(c_Nitpick_Orefl_H_type,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(c_Product__Type_Ointernal__split_type,type,
c_Product__Type_Ointernal__split: $i > $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OLin_type,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).
thf(645,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(244,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_OwfP @ B @ ( c_FunDef_Oin__rel @ B @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__in__rel) ).
thf(1322,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_OwfP @ B @ ( c_FunDef_Oin__rel @ B @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
thf(1024,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ E @ D ) @ ( hAPP @ E @ C ) )
=> ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__less) ).
thf(1823,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ E @ D ) @ ( hAPP @ E @ C ) )
=> ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
thf(1559,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Order__Relation_Opartial__order__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_member @ D @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_member @ D @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Partial__order__eq__Image1__Image1__iff) ).
thf(1729,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Order__Relation_Opartial__order__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_member @ D @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_member @ D @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( ( ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(396,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__empty) ).
thf(1899,plain,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(383,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
<=> ( ( C = B )
| ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(1850,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
=> ( ( C = B )
| ( c_member @ D @ C @ A ) ) )
& ( ( ( C = B )
| ( c_member @ D @ C @ A ) )
=> ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(7,axiom,
class_Orderings_Oord @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(555,plain,
class_Orderings_Oord @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__mono) ).
thf(1168,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__cancel) ).
thf(760,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
<=> ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ A @ D ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__singleton__iff) ).
thf(2131,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ A @ D ) @ B ) )
& ( ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ A @ D ) @ B )
=> ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(277,axiom,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ A @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).
thf(1454,plain,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ A @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
<=> ( c_Orderings_Oord__class_Oless @ E @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
thf(1083,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
=> ( c_Orderings_Oord__class_Oless @ E @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ E @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(962,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Owell__order__on @ C @ B @ A )
<=> ( ( c_Order__Relation_Olinear__order__on @ C @ B @ A )
& ( c_Wellfounded_Owf @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_well__order__on__def) ).
thf(1982,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Order__Relation_Owell__order__on @ C @ B @ A )
=> ( ( c_Order__Relation_Olinear__order__on @ C @ B @ A )
& ( c_Wellfounded_Owf @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ C ) ) ) ) )
& ( ( ( c_Order__Relation_Olinear__order__on @ C @ B @ A )
& ( c_Wellfounded_Owf @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ C ) ) ) )
=> ( c_Order__Relation_Owell__order__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I8_J) ).
thf(666,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Relation_Osingle__valued @ F @ E @ D )
=> ( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ C @ B ) @ D )
=> ( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ C @ A ) @ D )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedD) ).
thf(1818,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Relation_Osingle__valued @ F @ E @ D )
=> ( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ C @ B ) @ D )
=> ( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ C @ A ) @ D )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Wellfounded_Oacc @ D @ B ) )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ C ) @ B )
=> ( c_member @ D @ A @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downward) ).
thf(2363,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Wellfounded_Oacc @ D @ B ) )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ C ) @ B )
=> ( c_member @ D @ A @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1I2) ).
thf(1005,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(458,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__empty) ).
thf(2117,plain,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
thf(683,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
thf(730,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI) ).
thf(1443,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__least) ).
thf(1401,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
<=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( c_Product__Type_OPair @ B @ A @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(1939,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( c_Product__Type_OPair @ B @ A @ D @ E ) ) ) )
& ( ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( c_Product__Type_OPair @ B @ A @ D @ E ) ) )
=> ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( c_Set_Oinsert @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff__single) ).
thf(741,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= ( c_Set_Oinsert @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(453,axiom,
( c_FunDef_Omax__strict
= ( c_Wellfounded_Omax__ext @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__strict__def) ).
thf(2099,plain,
( c_FunDef_Omax__strict
= ( c_Wellfounded_Omax__ext @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
thf(655,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
| ( B = A ) )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
thf(597,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__supI2) ).
thf(1173,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(418,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ A )
=> ( ( c_Set_Oinsert @ C @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(1971,plain,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ A )
=> ( ( c_Set_Oinsert @ C @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).
thf(1533,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
thf(614,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ B @ A )
=> ( c_member @ ( tc_prod @ C @ C ) @ B @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
thf(1692,plain,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ B @ A )
=> ( c_member @ ( tc_prod @ C @ C ) @ B @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
thf(677,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( A = B ) )
& ( ( A = B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(319,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ C ) )
=> ( ! [F: $i,G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ G ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ G @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ G ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__induct) ).
thf(1608,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ C ) )
=> ( ! [F: $i,G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ G ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ G @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ G ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ ( c_Relation_OImage @ C @ C @ B @ A ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfE__pf) ).
thf(1310,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ ( c_Relation_OImage @ C @ C @ B @ A ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
thf(550,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(349,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ D @ B ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ C @ A ) ) @ c_FunDef_Opair__less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__lessI2) ).
thf(1735,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ D @ B ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ C @ A ) ) @ c_FunDef_Opair__less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Relation_Orel__comp @ D @ D @ D @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) )
=> ( ( ( c_Relation_Orel__comp @ D @ D @ D @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) )
=> ( ( c_Relation_Orel__comp @ D @ D @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_union__comp__emptyR) ).
thf(2184,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Relation_Orel__comp @ D @ D @ D @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) )
=> ( ( ( c_Relation_Orel__comp @ D @ D @ D @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) )
=> ( ( c_Relation_Orel__comp @ D @ D @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(96,axiom,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
thf(814,plain,
! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Relation_Oantisym @ C @ A )
=> ( c_Relation_Oantisym @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__subset) ).
thf(1988,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Relation_Oantisym @ C @ A )
=> ( c_Relation_Oantisym @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(747,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
thf(1458,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(50,axiom,
class_Orderings_Oorder @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(670,plain,
class_Orderings_Oorder @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
thf(1078,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(363,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Relation_OId @ B ) @ ( c_Relation_Orel__comp @ B @ B @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__unfold) ).
thf(1788,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Relation_OId @ B ) @ ( c_Relation_Orel__comp @ B @ B @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Diff) ).
thf(1507,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(520,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ B ) @ A )
=> ( c_member @ C @ D @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ( c_member @ C @ B @ ( c_Wellfounded_Oacc @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_OaccI) ).
thf(2360,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ B ) @ A )
=> ( c_member @ C @ D @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ( c_member @ C @ B @ ( c_Wellfounded_Oacc @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Nitpick_Owf__wfrec_H @ E @ D @ C @ B @ A )
= ( hAPP @ ( hAPP @ B @ ( c_Recdef_Ocut @ E @ D @ ( c_Nitpick_Owf__wfrec @ E @ D @ C @ B ) @ C @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Owf__wfrec_H__def) ).
thf(1196,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Nitpick_Owf__wfrec_H @ E @ D @ C @ B @ A )
= ( hAPP @ ( hAPP @ B @ ( c_Recdef_Ocut @ E @ D @ ( c_Nitpick_Owf__wfrec @ E @ D @ C @ B ) @ C @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ ( c_fequal @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(1835,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_member @ C @ B @ ( c_fequal @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( c_member @ C @ B @ ( c_fequal @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oantisym @ D @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisymD) ).
thf(1782,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oantisym @ D @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
thf(1441,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ( c_member @ D @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
<=> ( ? [E: $i] :
( ( c_member @ D @ E @ C )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
| ? [E: $i] :
( ( c_member @ D @ E @ B )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bex__Un) ).
thf(973,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( c_member @ D @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
=> ( ? [E: $i] :
( ( c_member @ D @ E @ C )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
| ? [E: $i] :
( ( c_member @ D @ E @ B )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) )
& ( ( ? [E: $i] :
( ( c_member @ D @ E @ C )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
| ? [E: $i] :
( ( c_member @ D @ E @ B )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) )
=> ? [E: $i] :
( ( c_member @ D @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( c_member @ B @ D @ A )
<=> ( c_member @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(1613,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( c_member @ B @ D @ A )
=> ( c_member @ B @ C @ A ) )
& ( ( c_member @ B @ C @ A )
=> ( c_member @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).
thf(1724,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mono) ).
thf(2067,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ A ) @ B )
= ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) )
& ( ~ ( c_member @ D @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ A ) @ B )
= ( c_Set_Oinsert @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff__if) ).
thf(1887,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ A ) @ B )
= ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) )
& ( ~ ( c_member @ D @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ A ) @ B )
= ( c_Set_Oinsert @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
thf(651,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Ointernal__split @ F @ E @ D @ C @ ( c_Product__Type_OPair @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__conv) ).
thf(2227,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Ointernal__split @ F @ E @ D @ C @ ( c_Product__Type_OPair @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Olinear__order__on @ C @ B @ A )
<=> ( ( c_Order__Relation_Opartial__order__on @ C @ B @ A )
& ( c_Relation_Ototal__on @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linear__order__on__def) ).
thf(1391,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Order__Relation_Olinear__order__on @ C @ B @ A )
=> ( ( c_Order__Relation_Opartial__order__on @ C @ B @ A )
& ( c_Relation_Ototal__on @ C @ B @ A ) ) )
& ( ( ( c_Order__Relation_Opartial__order__on @ C @ B @ A )
& ( c_Relation_Ototal__on @ C @ B @ A ) )
=> ( c_Order__Relation_Olinear__order__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Opreorder__on @ C @ B @ A )
<=> ( ( c_Relation_Orefl__on @ C @ B @ A )
& ( c_Relation_Otrans @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_preorder__on__def) ).
thf(2010,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Order__Relation_Opreorder__on @ C @ B @ A )
=> ( ( c_Relation_Orefl__on @ C @ B @ A )
& ( c_Relation_Otrans @ C @ A ) ) )
& ( ( ( c_Relation_Orefl__on @ C @ B @ A )
& ( c_Relation_Otrans @ C @ A ) )
=> ( c_Order__Relation_Opreorder__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(406,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ORange @ E @ D @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( c_Relation_ORange @ E @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__insert) ).
thf(1935,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ORange @ E @ D @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( c_Relation_ORange @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( c_member @ B @ C @ A )
<=> ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__in__conv) ).
thf(1650,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( c_member @ B @ C @ A )
=> ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ? [C: $i] : ( c_member @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( ~ ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnE) ).
thf(1645,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( ~ ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
<=> ( ( C = B )
| ( ( C != B )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
thf(2136,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( C = B )
| ( ( C != B )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) )
& ( ( ( C = B )
| ( ( C != B )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ D @ B ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ C @ A ) ) @ c_FunDef_Opair__less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__lessI1) ).
thf(1904,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ D @ B ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ C @ A ) ) @ c_FunDef_Opair__less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(293,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__empty) ).
thf(1518,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ ( c_Relation_ODomain @ D @ D @ B ) )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
thf(1703,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ ( c_Relation_ODomain @ D @ D @ B ) )
=> ( ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(325,axiom,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__empty) ).
thf(1628,plain,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Ototal__on @ C @ B @ A )
<=> ! [D: $i] :
( ( c_member @ C @ D @ B )
=> ! [E: $i] :
( ( c_member @ C @ E @ B )
=> ( ( D != E )
=> ( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ E ) @ A )
| ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ E @ D ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__def) ).
thf(1709,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Ototal__on @ C @ B @ A )
=> ! [D: $i] :
( ( c_member @ C @ D @ B )
=> ! [E: $i] :
( ( c_member @ C @ E @ B )
=> ( ( D != E )
=> ( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ E ) @ A )
| ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ E @ D ) @ A ) ) ) ) ) )
& ( ! [D: $i] :
( ( c_member @ C @ D @ B )
=> ! [E: $i] :
( ( c_member @ C @ E @ B )
=> ( ( D != E )
=> ( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ E ) @ A )
| ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ E @ D ) @ A ) ) ) ) )
=> ( c_Relation_Ototal__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ ( c_Wellfounded_Oacc @ C @ A ) )
<=> ! [D: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ B ) @ A )
=> ( c_member @ C @ D @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_Osimps) ).
thf(2328,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_member @ C @ B @ ( c_Wellfounded_Oacc @ C @ A ) )
=> ! [D: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ B ) @ A )
=> ( c_member @ C @ D @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
& ( ! [D: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ B ) @ A )
=> ( c_member @ C @ D @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ( c_member @ C @ B @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I6_J) ).
thf(570,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__absorb1) ).
thf(1430,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( c_member @ D @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffD1) ).
thf(2039,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( c_member @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ? [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ A )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD) ).
thf(1660,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ? [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ A )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Product__Type_OPair @ F @ E @ D @ C )
= ( c_Product__Type_OPair @ F @ E @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(2339,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Product__Type_OPair @ F @ E @ D @ C )
= ( c_Product__Type_OPair @ F @ E @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ E ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__trancl__rD) ).
thf(1871,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ E ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(481,axiom,
! [A: $i,B: $i] :
( ( c_Nitpick_Orefl_H @ B @ A )
<=> ! [C: $i] : ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
thf(2217,plain,
! [A: $i,B: $i] :
( ( ( c_Nitpick_Orefl_H @ B @ A )
=> ! [C: $i] : ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ A ) )
& ( ! [C: $i] : ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ A )
=> ( c_Nitpick_Orefl_H @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( c_Recdef_Owfrec @ E @ D @ C @ B ) )
=> ( ( c_Wellfounded_Owf @ E @ C )
=> ( ( hAPP @ F @ A )
= ( hAPP @ ( hAPP @ B @ ( c_Recdef_Ocut @ E @ D @ F @ C @ A ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__wfrec) ).
thf(917,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( c_Recdef_Owfrec @ E @ D @ C @ B ) )
=> ( ( c_Wellfounded_Owf @ E @ C )
=> ( ( hAPP @ F @ A )
= ( hAPP @ ( hAPP @ B @ ( c_Recdef_Ocut @ E @ D @ F @ C @ A ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
thf(1313,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( B = A ) )
& ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ F @ E @ D @ C @ ( c_Product__Type_OPair @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(1832,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ F @ E @ D @ C @ ( c_Product__Type_OPair @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Otrans @ E @ D )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ B ) @ D )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ D )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transD) ).
thf(1992,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Otrans @ E @ D )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ B ) @ D )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ D )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(187,axiom,
! [A: $i,B: $i] : ( c_Relation_Ototal__on @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__empty) ).
thf(1132,plain,
! [A: $i,B: $i] : ( c_Relation_Ototal__on @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(69,axiom,
class_Lattices_Osemilattice__sup @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
thf(724,plain,
class_Lattices_Osemilattice__sup @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
thf(1055,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) )
=> ( ( c_Transitive__Closure_Ortrancl @ C @ A )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
thf(1409,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) )
=> ( ( c_Transitive__Closure_Ortrancl @ C @ A )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__assoc) ).
thf(638,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(220,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Relation_ODomain @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__domain) ).
thf(1247,plain,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Relation_ODomain @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ A )
= ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__idemp) ).
thf(1319,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ A )
= ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(250,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__refl) ).
thf(1347,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Order__Relation_Opreorder__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ D @ C @ B ) @ ( c_Relation_OImage @ D @ D @ C @ A ) )
<=> ! [E: $i] :
( ( c_member @ D @ E @ B )
=> ? [F: $i] :
( ( c_member @ D @ F @ A )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ F @ E ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__Image__Image__iff) ).
thf(2158,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Order__Relation_Opreorder__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ D @ C @ B ) @ ( c_Relation_OImage @ D @ D @ C @ A ) )
=> ! [E: $i] :
( ( c_member @ D @ E @ B )
=> ? [F: $i] :
( ( c_member @ D @ F @ A )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ F @ E ) @ C ) ) ) )
& ( ! [E: $i] :
( ( c_member @ D @ E @ B )
=> ? [F: $i] :
( ( c_member @ D @ F @ A )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ F @ E ) @ C ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ D @ C @ B ) @ ( c_Relation_OImage @ D @ D @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
=> ( c_member @ E @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD1) ).
thf(1773,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
=> ( c_member @ E @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(359,axiom,
! [A: $i] : ( c_Order__Relation_Owell__order__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_well__order__on__empty) ).
thf(1778,plain,
! [A: $i] : ( c_Order__Relation_Owell__order__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(482,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) )
=> ( ! [I: $i,J: $i,K: $i,L: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ I @ J ) @ ( c_Product__Type_OPair @ H @ G @ K @ L ) ) @ B )
=> ( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ K @ L ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).
thf(2222,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) )
=> ( ! [I: $i,J: $i,K: $i,L: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ I @ J ) @ ( c_Product__Type_OPair @ H @ G @ K @ L ) ) @ B )
=> ( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ K @ L ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Osemilattice__sup @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ E @ D @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__mono) ).
thf(1415,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Osemilattice__sup @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ E @ D @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supI) ).
thf(924,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( hAPP @ ( c_Wellfounded_Omeasure @ D ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ C ) @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measure) ).
thf(1946,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( hAPP @ ( c_Wellfounded_Omeasure @ D ) @ A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ C ) @ ( hAPP @ A @ B ) ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ C ) @ ( hAPP @ A @ B ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( hAPP @ ( c_Wellfounded_Omeasure @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(435,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Recdef_Ocut @ F @ E @ D @ C @ B )
= ( c_Recdef_Ocut @ F @ E @ A @ C @ B ) )
<=> ! [G: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ G @ B ) @ C )
=> ( ( hAPP @ D @ G )
= ( hAPP @ A @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cuts__eq) ).
thf(2027,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Recdef_Ocut @ F @ E @ D @ C @ B )
= ( c_Recdef_Ocut @ F @ E @ A @ C @ B ) )
=> ! [G: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ G @ B ) @ C )
=> ( ( hAPP @ D @ G )
= ( hAPP @ A @ G ) ) ) )
& ( ! [G: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ G @ B ) @ C )
=> ( ( hAPP @ D @ G )
= ( hAPP @ A @ G ) ) )
=> ( ( c_Recdef_Ocut @ F @ E @ D @ C @ B )
= ( c_Recdef_Ocut @ F @ E @ A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Ortrancl @ D @ B ) )
| ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Ortrancl @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rtrancl__UnI) ).
thf(2090,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Ortrancl @ D @ B ) )
| ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Ortrancl @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(1373,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(401,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( c_Relation_Otrans @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__reflclI) ).
thf(1911,plain,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( c_Relation_Otrans @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).
thf(623,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).
thf(1864,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i] : ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
thf(1828,plain,
! [A: $i,B: $i,C: $i] : ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI2) ).
thf(937,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1CI) ).
thf(1283,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(99,axiom,
! [A: $i] :
( ( c_Wellfounded_Omeasure @ A )
= ( c_Relation_Oinv__image @ tc_Nat_Onat @ A @ c_Wellfounded_Oless__than ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measure__def) ).
thf(821,plain,
! [A: $i] :
( ( c_Wellfounded_Omeasure @ A )
= ( c_Relation_Oinv__image @ tc_Nat_Onat @ A @ c_Wellfounded_Oless__than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ D @ C @ B ) @ A ) )
<=> ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).
thf(905,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ D @ C @ B ) @ A ) )
=> ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) ) )
& ( ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(1040,plain,
! [A: $i,B: $i] :
( ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(327,axiom,
! [A: $i,B: $i] : ( c_Relation_Oirrefl @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__diff__Id) ).
thf(1632,plain,
! [A: $i,B: $i] : ( c_Relation_Oirrefl @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ F @ E @ D )
=> ( ( c_member @ ( tc_prod @ F @ C ) @ ( c_Product__Type_OPair @ F @ C @ E @ B ) @ A )
=> ( c_member @ C @ B @ ( c_Relation_OImage @ F @ C @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__ImageI) ).
thf(2291,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ F @ E @ D )
=> ( ( c_member @ ( tc_prod @ F @ C ) @ ( c_Product__Type_OPair @ F @ C @ E @ B ) @ A )
=> ( c_member @ C @ B @ ( c_Relation_OImage @ F @ C @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Relation_Orel__comp @ C @ C @ C @ B @ A ) @ B )
=> ( c_FunDef_Oreduction__pair @ C @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduction__pairI) ).
thf(2254,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Relation_Orel__comp @ C @ C @ C @ B @ A ) @ B )
=> ( c_FunDef_Oreduction__pair @ C @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(311,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( c_member @ B @ C @ A )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
thf(1581,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( c_member @ B @ C @ A )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ! [C: $i] :
~ ( c_member @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Oacyclic @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ B )
=> ( c_Wellfounded_Oacyclic @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__subset) ).
thf(2335,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Oacyclic @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ B )
=> ( c_Wellfounded_Oacyclic @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(56,axiom,
class_Orderings_Olinorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(687,plain,
class_Orderings_Olinorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_OImage @ C @ C @ B @ A ) @ A )
=> ( ( c_Relation_OImage @ C @ C @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__closed__trancl) ).
thf(1377,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_OImage @ C @ C @ B @ A ) @ A )
=> ( ( c_Relation_OImage @ C @ C @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) )
<=> ( ( c_member @ ( tc_prod @ H @ H ) @ ( c_Product__Type_OPair @ H @ H @ F @ D ) @ B )
| ( ( F = D )
& ( c_member @ ( tc_prod @ G @ G ) @ ( c_Product__Type_OPair @ G @ G @ E @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lex__prod) ).
thf(2281,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) )
=> ( ( c_member @ ( tc_prod @ H @ H ) @ ( c_Product__Type_OPair @ H @ H @ F @ D ) @ B )
| ( ( F = D )
& ( c_member @ ( tc_prod @ G @ G ) @ ( c_Product__Type_OPair @ G @ G @ E @ C ) @ A ) ) ) )
& ( ( ( c_member @ ( tc_prod @ H @ H ) @ ( c_Product__Type_OPair @ H @ H @ F @ D ) @ B )
| ( ( F = D )
& ( c_member @ ( tc_prod @ G @ G ) @ ( c_Product__Type_OPair @ G @ G @ E @ C ) @ A ) ) )
=> ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( c_Relation_OImage @ B @ B @ ( c_Relation_OId @ B ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Id) ).
thf(877,plain,
! [A: $i,B: $i] :
( ( c_Relation_OImage @ B @ B @ ( c_Relation_OId @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I3_J) ).
thf(734,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_member @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ D )
=> ( ( c_member @ ( tc_prod @ G @ C ) @ ( c_Product__Type_OPair @ G @ C @ E @ B ) @ A )
=> ( c_member @ ( tc_prod @ H @ C ) @ ( c_Product__Type_OPair @ H @ C @ F @ B ) @ ( c_Relation_Orel__comp @ H @ G @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__compI) ).
thf(1622,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_member @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ D )
=> ( ( c_member @ ( tc_prod @ G @ C ) @ ( c_Product__Type_OPair @ G @ C @ E @ B ) @ A )
=> ( c_member @ ( tc_prod @ H @ C ) @ ( c_Product__Type_OPair @ H @ C @ F @ B ) @ ( c_Relation_Orel__comp @ H @ G @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(269,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Orderings_Obot__class_Obot @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__least) ).
thf(1433,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Orderings_Obot__class_Obot @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ E @ D ) @ ( hAPP @ E @ C ) )
=> ( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ A )
=> ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__leq) ).
thf(1600,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ E @ D ) @ ( hAPP @ E @ C ) )
=> ( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ A )
=> ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__least) ).
thf(1242,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(294,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__absorb2) ).
thf(1521,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ B )
=> ( c_Wellfounded_Owf @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__subset) ).
thf(1696,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ B )
=> ( c_Wellfounded_Owf @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( c_member @ B @ A @ D )
<=> ( c_member @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(1975,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( c_member @ B @ A @ D )
=> ( c_member @ B @ A @ C ) )
& ( ( c_member @ B @ A @ C )
=> ( c_member @ B @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).
thf(2002,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__empty) ).
thf(998,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singletonE) ).
thf(1074,plain,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD2) ).
thf(1206,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ ( c_Transitive__Closure_Ortrancl @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
thf(942,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ ( c_Transitive__Closure_Ortrancl @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_ODomain @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Un__eq) ).
thf(2204,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_ODomain @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Set_Oinsert @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( c_Set_Oinsert @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(1438,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Set_Oinsert @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( c_Set_Oinsert @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I4_J) ).
thf(546,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__is__Un) ).
thf(1338,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( c_member @ B @ A @ D )
=> ~ ( c_member @ B @ A @ C ) )
=> ~ ( ~ ( c_member @ B @ A @ D )
=> ( c_member @ B @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(2047,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( c_member @ B @ A @ D )
=> ~ ( c_member @ B @ A @ C ) )
=> ~ ( ~ ( c_member @ B @ A @ D )
=> ( c_member @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(450,axiom,
! [A: $i] : ( c_Wellfounded_Owf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__empty) ).
thf(2093,plain,
! [A: $i] : ( c_Wellfounded_Owf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A )
=> ( c_member @ E @ C @ ( c_Relation_ODomain @ E @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainI) ).
thf(2000,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A )
=> ( c_member @ E @ C @ ( c_Relation_ODomain @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
| ( B
= ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__singletonD) ).
thf(1199,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
| ( B
= ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ODomain @ E @ D @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A ) )
= ( c_Set_Oinsert @ E @ C @ ( c_Relation_ODomain @ E @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__insert) ).
thf(2164,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ODomain @ E @ D @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A ) )
= ( c_Set_Oinsert @ E @ C @ ( c_Relation_ODomain @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(485,axiom,
! [A: $i] :
( ( c_Relation_OId__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__empty) ).
thf(2232,plain,
! [A: $i] :
( ( c_Relation_OId__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).
thf(2296,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(93,axiom,
! [A: $i,B: $i] : ( c_Relation_Oantisym @ B @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__Id__on) ).
thf(798,plain,
! [A: $i,B: $i] : ( c_Relation_Oantisym @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(197,axiom,
! [A: $i,B: $i] : ( c_Relation_Osingle__valued @ B @ B @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
thf(1163,plain,
! [A: $i,B: $i] : ( c_Relation_Osingle__valued @ B @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(957,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
thf(1255,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B = A ) )
& ( ( B = A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(214,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__reflcl) ).
thf(1217,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(287,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(1502,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(10,axiom,
class_Groups_Ominus @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
thf(561,plain,
class_Groups_Ominus @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
thf(693,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(490,axiom,
! [A: $i] :
( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) )
=> ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ c_FunDef_Omin__strict ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smin__emptyI) ).
thf(2249,plain,
! [A: $i] :
( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) )
=> ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ c_FunDef_Omin__strict ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityI) ).
thf(1021,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Osingle__valued @ C @ B @ A )
<=> ! [D: $i,E: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ E ) @ A )
=> ! [F: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ F ) @ A )
=> ( E = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__def) ).
thf(1570,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Osingle__valued @ C @ B @ A )
=> ! [D: $i,E: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ E ) @ A )
=> ! [F: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ F ) @ A )
=> ( E = F ) ) ) )
& ( ! [D: $i,E: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ E ) @ A )
=> ! [F: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ F ) @ A )
=> ( E = F ) ) )
=> ( c_Relation_Osingle__valued @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ B @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
<=> ? [G: $i] :
( ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= ( hAPP @ ( hAPP @ C @ G ) @ B ) )
& ! [H: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ H @ B ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ H @ ( hAPP @ G @ H ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfrec__rel_Oequations) ).
thf(1676,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ B @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ? [G: $i] :
( ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= ( hAPP @ ( hAPP @ C @ G ) @ B ) )
& ! [H: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ H @ B ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ H @ ( hAPP @ G @ H ) ) ) ) )
& ( ? [G: $i] :
( ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= ( hAPP @ ( hAPP @ C @ G ) @ B ) )
& ! [H: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ H @ B ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ H @ ( hAPP @ G @ H ) ) ) )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ B @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(252,axiom,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__absorb) ).
thf(1365,plain,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
<=> ( ( c_member @ D @ C @ B )
| ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__iff) ).
thf(1920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( ( c_member @ D @ C @ B )
| ( c_member @ D @ C @ A ) ) )
& ( ( ( c_member @ D @ C @ B )
| ( c_member @ D @ C @ A ) )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Otrans @ D @ C )
=> ( ( c_Relation_Otrans @ B @ A )
=> ( c_Relation_Otrans @ ( tc_prod @ D @ B ) @ ( c_Wellfounded_Olex__prod @ D @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__lex__prod) ).
thf(1951,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Otrans @ D @ C )
=> ( ( c_Relation_Otrans @ B @ A )
=> ( c_Relation_Otrans @ ( tc_prod @ D @ B ) @ ( c_Wellfounded_Olex__prod @ D @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).
thf(1296,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ D @ B ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ C @ A ) ) @ c_FunDef_Opair__leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__leqI2) ).
thf(1687,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ D @ B ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ C @ A ) ) @ c_FunDef_Opair__leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(323,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
thf(1624,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__not__empty) ).
thf(1159,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
thf(1210,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
<=> ! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(757,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
=> ! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) ) )
& ( ! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oantisym @ B @ A )
<=> ! [C: $i,D: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ D ) @ A )
=> ( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ A )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__def) ).
thf(1634,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Oantisym @ B @ A )
=> ! [C: $i,D: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ D ) @ A )
=> ( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ A )
=> ( C = D ) ) ) )
& ( ! [C: $i,D: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ D ) @ A )
=> ( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ A )
=> ( C = D ) ) )
=> ( c_Relation_Oantisym @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( c_Set_Othe__elem @ B @ ( c_Set_Oinsert @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__elem__eq) ).
thf(842,plain,
! [A: $i,B: $i] :
( ( c_Set_Othe__elem @ B @ ( c_Set_Oinsert @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ D @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insert) ).
thf(1012,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(407,axiom,
c_FunDef_Oreduction__pair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ c_FunDef_Omax__strict @ c_FunDef_Omax__weak ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__rpair__set) ).
thf(1938,plain,
c_FunDef_Oreduction__pair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ c_FunDef_Omax__strict @ c_FunDef_Omax__weak ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(107,axiom,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Opred__nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pred__nat) ).
thf(847,plain,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Opred__nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert) ).
thf(1032,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ A ) )
<=> ? [F: $i] :
( ( c_member @ C @ F @ A )
& ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ F @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__iff) ).
thf(1602,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ A ) )
=> ? [F: $i] :
( ( c_member @ C @ F @ A )
& ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ F @ D ) @ B ) ) )
& ( ? [F: $i] :
( ( c_member @ C @ F @ A )
& ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ F @ D ) @ B ) )
=> ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(1,conjecture,
( ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [A: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ A ) @ v_L )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ v_L ) ) ) )
<=> ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [A: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ A ) @ v_L )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ v_L ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [A: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ A ) @ v_L )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ v_L ) ) ) )
<=> ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [A: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ A ) @ v_L )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ v_L ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(522,plain,
~ ( ( ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [A: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ A ) @ v_L )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ v_L ) ) ) )
=> ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [A: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ A ) @ v_L )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ v_L ) ) ) ) )
& ( ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [A: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ A ) @ v_L )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ v_L ) ) ) )
=> ( ( c_Relation_Otrans @ tc_Arrow__Order__Mirabelle_Oalt @ v_L )
& ! [A: $i] :
~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ A ) @ v_L )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ v_L )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ v_L ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityE) ).
thf(830,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(121,axiom,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Oless__than,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__less__than) ).
thf(889,plain,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Oless__than,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ~ ( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffE) ).
thf(2179,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ~ ( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnI1) ).
thf(2313,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supI2) ).
thf(1128,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ A )
<=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
thf(2112,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_member @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ A @ B ) ) )
& ( ( hBOOL @ ( hAPP @ A @ B ) )
=> ( c_member @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty__left) ).
thf(1291,plain,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ A )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtranclE) ).
thf(1541,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ A )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ B ) @ A )
= ( c_Set_Oinsert @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__insert__left) ).
thf(874,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ B ) @ A )
= ( c_Set_Oinsert @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Product__Type_OPair @ F @ E @ D @ C )
= ( c_Product__Type_OPair @ F @ E @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(1762,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Product__Type_OPair @ F @ E @ D @ C )
= ( c_Product__Type_OPair @ F @ E @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Product__Type_OPair @ F @ E @ D @ C )
= ( c_Product__Type_OPair @ F @ E @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
thf(948,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Orefl__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_Relation_Oantisym @ D @ C )
=> ( ( c_member @ D @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_member @ D @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
<=> ( B = A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Refl__antisym__eq__Image1__Image1__iff) ).
thf(1953,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Orefl__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_Relation_Oantisym @ D @ C )
=> ( ( c_member @ D @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_member @ D @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( ( ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(367,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ A @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__irrefl) ).
thf(1804,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ A @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ominus @ B )
=> ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
thf(725,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ominus @ B )
=> ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_prod @ D @ B ) @ ( c_Wellfounded_Olex__prod @ D @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lex__prod) ).
thf(1878,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_prod @ D @ B ) @ ( c_Wellfounded_Olex__prod @ D @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(25,axiom,
class_Orderings_Opreorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(593,plain,
class_Orderings_Opreorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Diff__cancel2) ).
thf(869,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(30,axiom,
class_Orderings_Oorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(610,plain,
class_Orderings_Oorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ B @ D )
=> ! [E: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ B @ A @ D @ C ) @ E )
= ( hAPP @ ( hAPP @ C @ ( c_Recdef_Ocut @ B @ A @ ( c_Recdef_Owfrec @ B @ A @ D @ C ) @ D @ E ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__wfrec) ).
thf(989,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ B @ D )
=> ! [E: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ B @ A @ D @ C ) @ E )
= ( hAPP @ ( hAPP @ C @ ( c_Recdef_Ocut @ B @ A @ ( c_Recdef_Owfrec @ B @ A @ D @ C ) @ D @ E ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
!= ( c_Set_Oinsert @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__not__insert) ).
thf(1397,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
!= ( c_Set_Oinsert @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Order__Relation_Opreorder__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_member @ D @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_member @ D @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
<=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__Image1__Image1__iff) ).
thf(2300,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Order__Relation_Opreorder__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_member @ D @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_member @ D @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C ) )
& ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Ocommute) ).
thf(578,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert2) ).
thf(783,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
thf(1118,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__eq) ).
thf(1493,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
& ( B != A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
& ( B != A ) )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__commute) ).
thf(884,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C @ B @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Product__Type_OPair @ E @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryE) ).
thf(1964,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C @ B @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Product__Type_OPair @ E @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__by__empty) ).
thf(933,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(49,axiom,
class_Orderings_Obot @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
thf(669,plain,
class_Orderings_Obot @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(41,axiom,
class_Orderings_Obot @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
thf(642,plain,
class_Orderings_Obot @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(379,axiom,
! [A: $i] : ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ c_FunDef_Omin__weak ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wmin__emptyI) ).
thf(1842,plain,
! [A: $i] : ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ c_FunDef_Omin__weak ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ A ) )
=> ~ ! [F: $i] :
( ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ F @ D ) @ B )
=> ~ ( c_member @ C @ F @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ImageE) ).
thf(1700,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ A ) )
=> ~ ! [F: $i] :
( ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ F @ D ) @ B )
=> ~ ( c_member @ C @ F @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(517,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
<=> ! [C: $i] : ( c_member @ B @ C @ ( c_Wellfounded_Oacc @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__acc__iff) ).
thf(2349,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Owf @ B @ A )
=> ! [C: $i] : ( c_member @ B @ C @ ( c_Wellfounded_Oacc @ B @ A ) ) )
& ( ! [C: $i] : ( c_member @ B @ C @ ( c_Wellfounded_Oacc @ B @ A ) )
=> ( c_Wellfounded_Owf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(352,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ E @ D ) @ C )
=> ( ( hAPP @ ( c_Recdef_Ocut @ F @ B @ A @ C @ D ) @ E )
= ( hAPP @ A @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cut__apply) ).
thf(1744,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ E @ D ) @ C )
=> ( ( hAPP @ ( c_Recdef_Ocut @ F @ B @ A @ C @ D ) @ E )
= ( hAPP @ A @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(65,axiom,
class_Orderings_Opreorder @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(706,plain,
class_Orderings_Opreorder @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__upper1) ).
thf(1419,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(6,axiom,
class_Lattices_Osemilattice__sup @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
thf(554,plain,
class_Lattices_Osemilattice__sup @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supI1) ).
thf(753,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( c_member @ B @ C @ A )
=> ( c_member @ B @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(1791,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( c_member @ B @ C @ A )
=> ( c_member @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ B @ A ) @ ( c_Relation_OId @ C ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__in__Id__conv) ).
thf(2172,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ B @ A ) @ ( c_Relation_OId @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ B @ A ) @ ( c_Relation_OId @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I5_J) ).
thf(590,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ D ) )
=> ( ! [F: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ F ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ! [G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ G ) @ B )
=> ( ( hBOOL @ ( hAPP @ A @ F ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__induct) ).
thf(2085,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ D ) )
=> ( ! [F: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ F ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ! [G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ G ) @ B )
=> ( ( hBOOL @ ( hAPP @ A @ F ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
thf(837,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).
thf(1263,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
thf(701,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
thf(1266,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(419,axiom,
c_Relation_Otrans @ tc_Nat_Onat @ c_Wellfounded_Oless__than,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__than) ).
thf(1974,plain,
c_Relation_Otrans @ tc_Nat_Onat @ c_Wellfounded_Oless__than,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ( ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclE) ).
thf(1932,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ( ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).
thf(1050,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(374,axiom,
! [A: $i] :
( ( c_Relation_OField @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__empty) ).
thf(1825,plain,
! [A: $i] :
( ( c_Relation_OField @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
<=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__Un__eq) ).
thf(1324,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= A ) )
& ( ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__upper2) ).
thf(1114,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ E @ D )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) )
| ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
thf(1588,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ E @ D )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) )
| ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ A @ C ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__mono) ).
thf(1099,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ A @ C ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(276,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
thf(1451,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__left__idem) ).
thf(738,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Obot @ C )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__apply) ).
thf(1530,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Obot @ C )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(301,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__asym) ).
thf(1539,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
thf(1456,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__ge1) ).
thf(1202,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnI2) ).
thf(2043,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__Diff) ).
thf(921,plain,
! [A: $i,B: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ F @ E @ D @ B ) @ ( c_Relation_OImage @ F @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__mono) ).
thf(1563,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ F @ E @ D @ B ) @ ( c_Relation_OImage @ F @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ B ) @ A )
<=> ( ( c_member @ D @ C @ A )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__subset) ).
thf(1187,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ B ) @ A )
=> ( ( c_member @ D @ C @ A )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) )
& ( ( ( c_member @ D @ C @ A )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ B @ A )
<=> ? [G: $i] :
( ( A
= ( hAPP @ ( hAPP @ C @ G ) @ B ) )
& ! [H: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ H @ B ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ H @ ( hAPP @ G @ H ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfrec__rel_Osimps) ).
thf(1663,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ B @ A )
=> ? [G: $i] :
( ( A
= ( hAPP @ ( hAPP @ C @ G ) @ B ) )
& ! [H: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ H @ B ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ H @ ( hAPP @ G @ H ) ) ) ) )
& ( ? [G: $i] :
( ( A
= ( hAPP @ ( hAPP @ C @ G ) @ B ) )
& ! [H: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ H @ B ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ H @ ( hAPP @ G @ H ) ) ) )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ A )
=> ( ( c_Set_Oinsert @ C @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff) ).
thf(1515,plain,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ A )
=> ( ( c_Set_Oinsert @ C @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( A != B )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
thf(1026,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( A != B )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(662,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
thf(926,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
thf(765,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(381,axiom,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__trancl) ).
thf(1846,plain,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(447,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
<=> ! [C: $i,D: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ D ) @ A )
=> ! [E: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ E ) @ A )
=> ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__def) ).
thf(2076,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Otrans @ B @ A )
=> ! [C: $i,D: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ D ) @ A )
=> ! [E: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ E ) @ A )
=> ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ E ) @ A ) ) ) )
& ( ! [C: $i,D: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ D ) @ A )
=> ! [E: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ E ) @ A )
=> ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ E ) @ A ) ) )
=> ( c_Relation_Otrans @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(200,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__reflcl) ).
thf(1170,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
<=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__sup) ).
thf(1286,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= A ) )
& ( ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(162,axiom,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__Id) ).
thf(1035,plain,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
<=> ( ( ( c_member @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) )
& ( ~ ( c_member @ D @ B @ A )
=> ( ( ( c_member @ D @ B @ C )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ A ) )
& ( ~ ( c_member @ D @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__insert__iff) ).
thf(1466,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
=> ( ( ( c_member @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) )
& ( ~ ( c_member @ D @ B @ A )
=> ( ( ( c_member @ D @ B @ C )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ A ) )
& ( ~ ( c_member @ D @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ) ) ) )
& ( ( ( ( c_member @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) )
& ( ~ ( c_member @ D @ B @ A )
=> ( ( ( c_member @ D @ B @ C )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ A ) )
& ( ~ ( c_member @ D @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ) ) )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__sup @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oidem) ).
thf(558,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__sup @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
thf(794,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Osemilattice__sup @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).
thf(586,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Osemilattice__sup @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ B @ ( c_Relation_OId__on @ C @ A ) )
=> ~ ! [D: $i] :
( ( c_member @ C @ D @ A )
=> ( B
!= ( c_Product__Type_OPair @ C @ C @ D @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__onE) ).
thf(2235,plain,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ B @ ( c_Relation_OId__on @ C @ A ) )
=> ~ ! [D: $i] :
( ( c_member @ C @ D @ A )
=> ( B
!= ( c_Product__Type_OPair @ C @ C @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate1D) ).
thf(1146,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(463,axiom,
( c_FunDef_Omin__strict
= ( c_Wellfounded_Omin__ext @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__strict__def) ).
thf(2149,plain,
( c_FunDef_Omin__strict
= ( c_Wellfounded_Omin__ext @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__absorb2) ).
thf(824,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__absorb1) ).
thf(1273,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(353,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ A )
<=> ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__def) ).
thf(1747,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Oacyclic @ B @ A )
=> ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) )
& ( ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(404,axiom,
! [A: $i,B: $i] :
( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ B @ A ) @ ( c_Transitive__Closure_Otrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq) ).
thf(1927,plain,
! [A: $i,B: $i] :
( ( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ B @ A ) @ ( c_Transitive__Closure_Otrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ B @ A ) @ ( c_Transitive__Closure_Otrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ G @ F ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( hAPP @ B @ F ) )
=> ( c_member @ ( tc_prod @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) @ ( c_Product__Type_OPair @ A @ E @ F @ D ) @ ( c_Product__Type_OPair @ A @ E @ F @ C ) ) @ ( c_Recdef_Osame__fst @ A @ E @ G @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__fstI) ).
thf(1595,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ G @ F ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( hAPP @ B @ F ) )
=> ( c_member @ ( tc_prod @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) @ ( c_Product__Type_OPair @ A @ E @ F @ D ) @ ( c_Product__Type_OPair @ A @ E @ F @ C ) ) @ ( c_Recdef_Osame__fst @ A @ E @ G @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(573,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
thf(689,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B = A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
thf(601,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( B = A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__trans) ).
thf(1278,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ A ) )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnCI) ).
thf(1906,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ A ) )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(750,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(290,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Relation_Oantisym @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).
thf(1510,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Relation_Oantisym @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Wellfounded_Oacc @ D @ B ) )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) )
=> ( c_member @ D @ A @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards) ).
thf(1698,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Wellfounded_Oacc @ D @ B ) )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) )
=> ( c_member @ D @ A @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( c_member @ C @ B @ ( c_Wellfounded_Oacc @ C @ A ) )
=> ~ ! [D: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ B ) @ A )
=> ( c_member @ C @ D @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__acc__down) ).
thf(1959,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( c_member @ C @ B @ ( c_Wellfounded_Oacc @ C @ A ) )
=> ~ ! [D: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ B ) @ A )
=> ( c_member @ C @ D @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( c_fequal @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(1103,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( c_fequal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Wellfounded_Omin__ext @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__ext__wf) ).
thf(819,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Wellfounded_Omin__ext @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(11,axiom,
class_Lattices_Olattice @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
thf(562,plain,
class_Lattices_Olattice @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__ge2) ).
thf(1007,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Otrans @ D @ C )
=> ( c_Relation_Otrans @ B @ ( hAPP @ ( c_Relation_Oinv__image @ D @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__inv__image) ).
thf(1620,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Otrans @ D @ C )
=> ( c_Relation_Otrans @ B @ ( hAPP @ ( c_Relation_Oinv__image @ D @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(354,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ D ) @ A )
=> ( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ A )
=> ( C = D ) ) )
=> ( c_Relation_Oantisym @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisymI) ).
thf(1752,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ D ) @ A )
=> ( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ A )
=> ( C = D ) ) )
=> ( c_Relation_Oantisym @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ B )
=> ( ~ ( c_member @ D @ C @ A )
=> ( ( ( c_Set_Oinsert @ D @ C @ B )
= ( c_Set_Oinsert @ D @ C @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(2016,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ B )
=> ( ~ ( c_member @ D @ C @ A )
=> ( ( ( ( c_Set_Oinsert @ D @ C @ B )
= ( c_Set_Oinsert @ D @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Set_Oinsert @ D @ C @ B )
= ( c_Set_Oinsert @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1E) ).
thf(1388,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_Relation_Orefl__on @ E @ B @ A )
=> ( c_Relation_Orefl__on @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Un) ).
thf(1535,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_Relation_Orefl__on @ E @ B @ A )
=> ( c_Relation_Orefl__on @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
thf(1403,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C @ B @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Product__Type_OPair @ E @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryD) ).
thf(1795,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C @ B @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Product__Type_OPair @ E @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__inject) ).
thf(1124,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).
thf(1488,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
thf(584,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__trans) ).
thf(1154,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(40,axiom,
class_Lattices_Olattice @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
thf(641,plain,
class_Lattices_Olattice @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_ORange @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_ORange @ D @ C @ B ) @ ( c_Relation_ORange @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Un__eq) ).
thf(2293,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_ORange @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_ORange @ D @ C @ B ) @ ( c_Relation_ORange @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__sup @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__idem) ).
thf(611,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__sup @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( B != A )
<=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
thf(713,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) )
=> ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
thf(1464,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FunDef_Oreduction__pair @ D @ C )
=> ( c_FunDef_Oreduction__pair @ B @ ( c_FunDef_Orp__inv__image @ D @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
thf(1271,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FunDef_Oreduction__pair @ D @ C )
=> ( c_FunDef_Oreduction__pair @ B @ ( c_FunDef_Orp__inv__image @ D @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).
thf(2308,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( c_member @ D @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
<=> ( ! [E: $i] :
( ( c_member @ D @ E @ C )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
& ! [E: $i] :
( ( c_member @ D @ E @ B )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ball__Un) ).
thf(1058,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( c_member @ D @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
=> ( ! [E: $i] :
( ( c_member @ D @ E @ C )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
& ! [E: $i] :
( ( c_member @ D @ E @ B )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) ) )
& ( ( ! [E: $i] :
( ( c_member @ D @ E @ C )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
& ! [E: $i] :
( ( c_member @ D @ E @ B )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) )
=> ! [E: $i] :
( ( c_member @ D @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
thf(1107,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( ( D = C )
=> ( B = A ) )
& ( ( B = A )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(217,axiom,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty__right) ).
thf(1239,plain,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_OField @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OField @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__insert) ).
thf(1997,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_OField @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OField @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
thf(900,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(464,axiom,
c_Wellfounded_Owf @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pair__less) ).
thf(2151,plain,
c_Wellfounded_Owf @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__less,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(395,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oirrefl @ B @ A )
<=> ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__def) ).
thf(1894,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Oirrefl @ B @ A )
=> ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ A ) )
& ( ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ A )
=> ( c_Relation_Oirrefl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
<=> ( ( c_member @ D @ C @ B )
& ~ ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__iff) ).
thf(1806,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( ( c_member @ D @ C @ B )
& ~ ( c_member @ D @ C @ A ) ) )
& ( ( ( c_member @ D @ C @ B )
& ~ ( c_member @ D @ C @ A ) )
=> ( c_member @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Transitive__Closure_Ortrancl @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
= ( c_Transitive__Closure_Ortrancl @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__rtrancl) ).
thf(1524,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Transitive__Closure_Ortrancl @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
= ( c_Transitive__Closure_Ortrancl @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oassoc) ).
thf(567,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ D @ A )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
thf(1144,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ D @ A )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
thf(599,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Set_Oinsert @ E @ D @ ( c_Set_Oinsert @ E @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Set_Oinsert @ E @ B @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
<=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
thf(1349,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( c_Set_Oinsert @ E @ D @ ( c_Set_Oinsert @ E @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Set_Oinsert @ E @ B @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) )
& ( ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) )
=> ( ( c_Set_Oinsert @ E @ D @ ( c_Set_Oinsert @ E @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Set_Oinsert @ E @ B @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Otrancl @ D @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__mono) ).
thf(2097,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Otrancl @ D @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__trancl) ).
thf(880,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
thf(649,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(616,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(183,axiom,
( c_Wellfounded_Oless__than
= ( c_Transitive__Closure_Otrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__than__def) ).
thf(1122,plain,
( c_Wellfounded_Oless__than
= ( c_Transitive__Closure_Otrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(475,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ E ) @ A )
=> ! [F: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ F ) @ A )
=> ( E = F ) ) )
=> ( c_Relation_Osingle__valued @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedI) ).
thf(2197,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ E ) @ A )
=> ! [F: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ F ) @ A )
=> ( E = F ) ) )
=> ( c_Relation_Osingle__valued @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
thf(1969,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ORange @ C @ D @ B ) @ ( c_Relation_ORange @ C @ D @ A ) ) @ ( c_Relation_ORange @ C @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Diff__subset) ).
thf(863,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ORange @ C @ D @ B ) @ ( c_Relation_ORange @ C @ D @ A ) ) @ ( c_Relation_ORange @ C @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Relation_Osingle__valued @ D @ C @ A )
=> ( c_Relation_Osingle__valued @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__subset) ).
thf(2065,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Relation_Osingle__valued @ D @ C @ A )
=> ( c_Relation_Osingle__valued @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ F @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
thf(1175,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ F @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(890,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ D @ C )
=> ( ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ B @ D ) @ c_FunDef_Opair__less )
=> ( ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ A @ C ) @ c_FunDef_Omax__strict )
=> ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ B @ A ) @ C ) @ c_FunDef_Omax__strict ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smax__insertI) ).
thf(2182,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ D @ C )
=> ( ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ B @ D ) @ c_FunDef_Opair__less )
=> ( ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ A @ C ) @ c_FunDef_Omax__strict )
=> ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ B @ A ) @ C ) @ c_FunDef_Omax__strict ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(171,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ A @ ( c_Orderings_Obot__class_Obot @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__bot__right) ).
thf(1080,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ A @ ( c_Orderings_Obot__class_Obot @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I2_J) ).
thf(631,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( C = A )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(97,axiom,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(816,plain,
! [A: $i] :
~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(326,axiom,
! [A: $i] : ( c_Order__Relation_Olinear__order__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lnear__order__on__empty) ).
thf(1630,plain,
! [A: $i] : ( c_Order__Relation_Olinear__order__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(496,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( c_member @ B @ D @ A )
=> ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ ( c_Relation_OId__on @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
thf(2267,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( c_member @ B @ D @ A )
=> ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ ( c_Relation_OId__on @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ A @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__not__refl) ).
thf(1909,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ A @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
<=> ( ( ( c_member @ D @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ A ) )
& ( ~ ( c_member @ D @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insert__iff) ).
thf(848,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
=> ( ( ( c_member @ D @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ A ) )
& ( ~ ( c_member @ D @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ) )
& ( ( ( ( c_member @ D @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ A ) )
& ( ~ ( c_member @ D @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( c_member @ C @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ C @ B @ A ) @ ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert__absorb) ).
thf(1029,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( c_member @ C @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ C @ B @ A ) @ ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).
thf(1344,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(1460,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ E @ D ) @ ( c_Wellfounded_Omax__ext @ F @ C ) )
=> ( ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ B @ A ) @ ( c_Wellfounded_Omax__ext @ F @ C ) )
=> ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) @ E @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) @ D @ A ) ) @ ( c_Wellfounded_Omax__ext @ F @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext__additive) ).
thf(2252,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ E @ D ) @ ( c_Wellfounded_Omax__ext @ F @ C ) )
=> ( ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ B @ A ) @ ( c_Wellfounded_Omax__ext @ F @ C ) )
=> ( c_member @ ( tc_prod @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) @ E @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ tc_HOL_Obool ) @ D @ A ) ) @ ( c_Wellfounded_Omax__ext @ F @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
<=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
thf(1177,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(372,axiom,
( c_FunDef_Opair__leq
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ tc_HOL_Obool ) @ c_FunDef_Opair__less @ ( c_Relation_OId @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__leq__def) ).
thf(1821,plain,
( c_FunDef_Opair__leq
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ tc_HOL_Obool ) @ c_FunDef_Opair__less @ ( c_Relation_OId @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
thf(594,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( c_Relation_OField @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ B @ B @ A ) @ ( c_Relation_ORange @ B @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__def) ).
thf(1149,plain,
! [A: $i,B: $i] :
( ( c_Relation_OField @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ B @ B @ A ) @ ( c_Relation_ORange @ B @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(964,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
& ( B != A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
& ( B != A ) )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
thf(685,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B @ A ) ) )
=> ( ! [F: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ F ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ! [G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ G ) @ A )
=> ( F = G ) ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__separatorE) ).
thf(2212,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B @ A ) ) )
=> ( ! [F: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ F ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ! [G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ G ) @ A )
=> ( F = G ) ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
thf(1445,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(780,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ~ ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
thf(1015,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ~ ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ~ ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(12,axiom,
class_Orderings_Oord @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(563,plain,
class_Orderings_Oord @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) @ ( c_Product__Type_OPair @ G @ F @ E @ D ) @ ( c_Product__Type_OPair @ G @ F @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) )
=> ( ( ( c_Product__Type_OPair @ G @ F @ E @ D )
!= ( c_Product__Type_OPair @ G @ F @ C @ B ) )
=> ~ ! [H: $i,I: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) @ ( c_Product__Type_OPair @ G @ F @ E @ D ) @ ( c_Product__Type_OPair @ G @ F @ H @ I ) ) @ A )
=> ~ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) @ ( c_Product__Type_OPair @ G @ F @ H @ I ) @ ( c_Product__Type_OPair @ G @ F @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).
thf(2022,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) @ ( c_Product__Type_OPair @ G @ F @ E @ D ) @ ( c_Product__Type_OPair @ G @ F @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) )
=> ( ( ( c_Product__Type_OPair @ G @ F @ E @ D )
!= ( c_Product__Type_OPair @ G @ F @ C @ B ) )
=> ~ ! [H: $i,I: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) @ ( c_Product__Type_OPair @ G @ F @ E @ D ) @ ( c_Product__Type_OPair @ G @ F @ H @ I ) ) @ A )
=> ~ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) @ ( c_Product__Type_OPair @ G @ F @ H @ I ) @ ( c_Product__Type_OPair @ G @ F @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ E @ D ) @ ( hAPP @ ( c_Relation_Oinv__image @ C @ F @ B ) @ A ) )
<=> ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ ( hAPP @ A @ E ) @ ( hAPP @ A @ D ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__inv__image) ).
thf(2101,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ E @ D ) @ ( hAPP @ ( c_Relation_Oinv__image @ C @ F @ B ) @ A ) )
=> ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ ( hAPP @ A @ E ) @ ( hAPP @ A @ D ) ) @ B ) )
& ( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ ( hAPP @ A @ E ) @ ( hAPP @ A @ D ) ) @ B )
=> ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ E @ D ) @ ( hAPP @ ( c_Relation_Oinv__image @ C @ F @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(505,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oantisym @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) )
<=> ( c_Relation_Oantisym @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__reflcl) ).
thf(2303,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Oantisym @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) )
=> ( c_Relation_Oantisym @ B @ A ) )
& ( ( c_Relation_Oantisym @ B @ A )
=> ( c_Relation_Oantisym @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ D @ C )
=> ( ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ D @ B ) @ c_FunDef_Opair__leq )
=> ( ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ C @ A ) @ c_FunDef_Omin__weak )
=> ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ B @ A ) ) @ c_FunDef_Omin__weak ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wmin__insertI) ).
thf(2156,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ D @ C )
=> ( ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ D @ B ) @ c_FunDef_Opair__leq )
=> ( ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ C @ A ) @ c_FunDef_Omin__weak )
=> ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ B @ A ) ) @ c_FunDef_Omin__weak ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(478,axiom,
! [A: $i] : ( c_Order__Relation_Opartial__order__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partial__order__on__empty) ).
thf(2207,plain,
! [A: $i] : ( c_Order__Relation_Opartial__order__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ~ ( c_member @ D @ C @ A )
=> ( c_member @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffI) ).
thf(1694,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ~ ( c_member @ D @ C @ A )
=> ( c_member @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ D @ C )
=> ( ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ D @ B ) @ c_FunDef_Opair__less )
=> ( ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ C @ A ) @ c_FunDef_Omin__strict )
=> ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ B @ A ) ) @ c_FunDef_Omin__strict ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smin__insertI) ).
thf(2069,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ D @ C )
=> ( ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ D @ B ) @ c_FunDef_Opair__less )
=> ( ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ C @ A ) @ c_FunDef_Omin__strict )
=> ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ B @ A ) ) @ c_FunDef_Omin__strict ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Relation_ORange @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__range) ).
thf(768,plain,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Relation_ORange @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
thf(827,plain,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Ocurry @ F @ E @ D @ C @ B @ A )
= ( hAPP @ C @ ( c_Product__Type_OPair @ F @ E @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__conv) ).
thf(1775,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Ocurry @ F @ E @ D @ C @ B @ A )
= ( hAPP @ C @ ( c_Product__Type_OPair @ F @ E @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supE) ).
thf(1435,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ G @ E ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ C @ D @ B @ G @ ( hAPP @ A @ G ) ) )
=> ( c_Recdef_Owfrec__rel @ F @ C @ D @ B @ E @ ( hAPP @ ( hAPP @ B @ A ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfrec__rel_Ointros) ).
thf(1726,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ G @ E ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ C @ D @ B @ G @ ( hAPP @ A @ G ) ) )
=> ( c_Recdef_Owfrec__rel @ F @ C @ D @ B @ E @ ( hAPP @ ( hAPP @ B @ A ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).
thf(1250,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(430,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( ( c_Transitive__Closure_Otrancl @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__id) ).
thf(2005,plain,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( ( c_Transitive__Closure_Otrancl @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubsetD) ).
thf(1626,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( class_Orderings_Obot @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
thf(722,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( class_Orderings_Obot @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( c_member @ E @ B @ D )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__equiv__class) ).
thf(2239,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( c_member @ E @ B @ D )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
thf(675,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
thf(944,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ C @ c_Arrow__Order__Mirabelle_OLin )
=> ( ( B != A )
=> ( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
thf(2271,plain,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ C @ c_Arrow__Order__Mirabelle_OLin )
=> ( ( B != A )
=> ( ( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ C ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ C )
=> ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ D @ B ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ C @ A ) ) @ c_FunDef_Opair__leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__leqI1) ).
thf(2037,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
=> ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ D @ B ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ C @ A ) ) @ c_FunDef_Opair__leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__iff) ).
thf(1134,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_member @ C @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( c_member @ C @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Wellfounded_Owf @ E @ D )
=> ( ( hAPP @ ( c_Recdef_Owfrec @ E @ C @ D @ B ) @ A )
= ( hAPP @ ( hAPP @ B @ ( c_Recdef_Ocut @ E @ C @ ( c_Recdef_Owfrec @ E @ C @ D @ B ) @ D @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfrec) ).
thf(939,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Wellfounded_Owf @ E @ D )
=> ( ( hAPP @ ( c_Recdef_Owfrec @ E @ C @ D @ B ) @ A )
= ( hAPP @ ( hAPP @ B @ ( c_Recdef_Ocut @ E @ C @ ( c_Recdef_Owfrec @ E @ C @ D @ B ) @ D @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(493,axiom,
! [A: $i,B: $i] :
( ! [C: $i] : ( c_member @ B @ C @ ( c_Wellfounded_Oacc @ B @ A ) )
=> ( c_Wellfounded_Owf @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__wfI) ).
thf(2256,plain,
! [A: $i,B: $i] :
( ! [C: $i] : ( c_member @ B @ C @ ( c_Wellfounded_Oacc @ B @ A ) )
=> ( c_Wellfounded_Owf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(304,axiom,
! [A: $i,B: $i] : ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ A @ A ) @ ( c_Relation_OId @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IdI) ).
thf(1551,plain,
! [A: $i,B: $i] : ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ A @ A ) @ ( c_Relation_OId @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(423,axiom,
! [A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__empty) ).
thf(1990,plain,
! [A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__trans) ).
thf(2202,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Wellfounded_Oacc @ C @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__subset) ).
thf(2298,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Wellfounded_Oacc @ C @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
thf(872,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__partition) ).
thf(1156,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
thf(887,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Relation_ODomain @ D @ B @ A ) )
=> ~ ! [E: $i] :
~ ( c_member @ ( tc_prod @ D @ B ) @ ( c_Product__Type_OPair @ D @ B @ C @ E ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainE) ).
thf(1647,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Relation_ODomain @ D @ B @ A ) )
=> ~ ! [E: $i] :
~ ( c_member @ ( tc_prod @ D @ B ) @ ( c_Product__Type_OPair @ D @ B @ C @ E ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
<=> ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
thf(1368,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Oordered__ab__group__add @ E )
=> ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
= ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_OField @ C @ B ) @ ( c_Relation_OField @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mono__Field) ).
thf(1780,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_OField @ C @ B ) @ ( c_Relation_OField @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(442,axiom,
! [A: $i,B: $i] :
( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ B @ A ) @ ( c_Transitive__Closure_Ortrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__nat__trancl__eq__le) ).
thf(2060,plain,
! [A: $i,B: $i] :
( ( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ B @ A ) @ ( c_Transitive__Closure_Ortrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ B @ A ) @ ( c_Transitive__Closure_Ortrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
thf(707,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B )
=> ( A = B ) )
& ( ( A = B )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ B @ A )
=> ( c_member @ ( tc_prod @ C @ C ) @ B @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
thf(1869,plain,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ B @ A )
=> ( c_member @ ( tc_prod @ C @ C ) @ B @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(514,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( ( c_Relation_Oantisym @ B @ A )
=> ( c_Relation_Otrans @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__diff__Id) ).
thf(2337,plain,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ A )
=> ( ( c_Relation_Oantisym @ B @ A )
=> ( c_Relation_Otrans @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( c_member @ D @ C @ B )
=> ( C = A ) )
=> ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertCI) ).
thf(2276,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( c_member @ D @ C @ B )
=> ( C = A ) )
=> ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(376,axiom,
! [A: $i] : ( c_Order__Relation_Opreorder__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_preorder__on__empty) ).
thf(1830,plain,
! [A: $i] : ( c_Order__Relation_Opreorder__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ D @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1I1) ).
thf(1130,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ D @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
thf(643,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ E @ B ) @ A ) )
<=> ( ( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= D ) )
| ? [H: $i,I: $i] :
( ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= ( hAPP @ ( hAPP @ E @ H ) @ I ) )
& ( c_member @ G @ H @ C )
& ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ G @ H @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).
thf(1220,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ E @ B ) @ A ) )
=> ( ( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= D ) )
| ? [H: $i,I: $i] :
( ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= ( hAPP @ ( hAPP @ E @ H ) @ I ) )
& ( c_member @ G @ H @ C )
& ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ G @ H @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ I ) ) ) )
& ( ( ( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) )
& ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= D ) )
| ? [H: $i,I: $i] :
( ( ( hAPP @ ( hAPP @ E @ B ) @ A )
= ( hAPP @ ( hAPP @ E @ H ) @ I ) )
& ( c_member @ G @ H @ C )
& ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ G @ H @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ I ) ) )
=> ( c_Nitpick_Ofold__graph_H @ G @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ E @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(518,axiom,
! [A: $i,B: $i] :
~ ( c_member @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__iff) ).
thf(2354,plain,
! [A: $i,B: $i] :
~ ( c_member @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(840,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ? [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD2) ).
thf(1785,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ? [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(576,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i] : ( c_member @ C @ B @ ( c_Set_Oinsert @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).
thf(1658,plain,
! [A: $i,B: $i,C: $i] : ( c_member @ C @ B @ ( c_Set_Oinsert @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Oacyclic @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) )
<=> ( ( c_Wellfounded_Oacyclic @ D @ A )
& ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__insert) ).
thf(2322,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Oacyclic @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) )
=> ( ( c_Wellfounded_Oacyclic @ D @ A )
& ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) )
& ( ( ( c_Wellfounded_Oacyclic @ D @ A )
& ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( c_Wellfounded_Oacyclic @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__mp) ).
thf(2247,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__reflcl__absorb) ).
thf(744,plain,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
thf(703,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A )
| ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__apply) ).
thf(1141,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(519,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_OField @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_OField @ C @ B ) @ ( c_Relation_OField @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__Un) ).
thf(2357,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_OField @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_OField @ C @ B ) @ ( c_Relation_OField @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__commute) ).
thf(727,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_ODomain @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).
thf(1797,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Relation_ODomain @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) )
=> ( ( c_Relation_ODomain @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__assoc) ).
thf(1485,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(510,axiom,
( c_FunDef_Omin__weak
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( c_Wellfounded_Omin__ext @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__leq ) @ ( c_Set_Oinsert @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__weak__def) ).
thf(2320,plain,
( c_FunDef_Omin__weak
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( c_Wellfounded_Omin__ext @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__leq ) @ ( c_Set_Oinsert @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate2D) ).
thf(1052,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).
thf(845,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty) ).
thf(1421,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I1_J) ).
thf(627,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(440,axiom,
! [A: $i] : ( c_Relation_Otrans @ A @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Id) ).
thf(2045,plain,
! [A: $i] : ( c_Relation_Otrans @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD1) ).
thf(1180,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__acyclic) ).
thf(931,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( C = B )
| ( ( C != B )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclD) ).
thf(1553,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( C = B )
| ( ( C != B )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
thf(671,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_ORange @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__empty__iff) ).
thf(1913,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Relation_ORange @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) )
=> ( ( c_Relation_ORange @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__left__commute) ).
thf(581,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
=> ( ( C != B )
=> ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertE) ).
thf(2209,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
=> ( ( C != B )
=> ( c_member @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Olinear__order__on @ C @ B @ A )
=> ( c_Order__Relation_Ostrict__linear__order__on @ C @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__linear__order__on__diff__Id) ).
thf(2110,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Olinear__order__on @ C @ B @ A )
=> ( c_Order__Relation_Ostrict__linear__order__on @ C @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
thf(771,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ F )
=> ( ( hAPP @ ( c_Recdef_Ocut @ D @ A @ E @ F @ B ) @ C )
= ( hAPP @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__cut__apply) ).
thf(1966,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ F )
=> ( ( hAPP @ ( c_Recdef_Ocut @ D @ A @ E @ F @ B ) @ C )
= ( hAPP @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
thf(556,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(507,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclicI) ).
thf(2310,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(380,axiom,
( c_FunDef_Omax__weak
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( c_Wellfounded_Omax__ext @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__leq ) @ ( c_Set_Oinsert @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__weak__def) ).
thf(1844,plain,
( c_FunDef_Omax__weak
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( c_Wellfounded_Omax__ext @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ c_FunDef_Opair__leq ) @ ( c_Set_Oinsert @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(57,axiom,
class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
thf(688,plain,
class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
thf(903,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Opreorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_member @ C @ A @ ( c_Wellfounded_Oacc @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__wfD) ).
thf(2347,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_member @ C @ A @ ( c_Wellfounded_Oacc @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_OImage @ E @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ E @ D @ C @ B ) @ ( c_Relation_OImage @ E @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Un) ).
thf(1412,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_OImage @ E @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ E @ D @ C @ B ) @ ( c_Relation_OImage @ E @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
thf(1448,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(474,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
<=> ! [C: $i] :
( ? [D: $i] : ( c_member @ B @ D @ C )
=> ? [D: $i] :
( ( c_member @ B @ D @ C )
& ! [E: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ E @ D ) @ A )
=> ~ ( c_member @ B @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).
thf(2187,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Owf @ B @ A )
=> ! [C: $i] :
( ? [D: $i] : ( c_member @ B @ D @ C )
=> ? [D: $i] :
( ( c_member @ B @ D @ C )
& ! [E: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ E @ D ) @ A )
=> ~ ( c_member @ B @ E @ C ) ) ) ) )
& ( ! [C: $i] :
( ? [D: $i] : ( c_member @ B @ D @ C )
=> ? [D: $i] :
( ( c_member @ B @ D @ C )
& ! [E: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ E @ D ) @ A )
=> ~ ( c_member @ B @ E @ C ) ) ) )
=> ( c_Wellfounded_Owf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(387,axiom,
! [A: $i,B: $i] :
~ ( c_member @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_emptyE) ).
thf(1866,plain,
! [A: $i,B: $i] :
~ ( c_member @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) )
=> ( ! [I: $i,J: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ I @ J ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ! [K: $i,L: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ I @ J ) @ ( c_Product__Type_OPair @ H @ G @ K @ L ) ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).
thf(2071,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) )
=> ( ! [I: $i,J: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ I @ J ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ! [K: $i,L: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ I @ J ) @ ( c_Product__Type_OPair @ H @ G @ K @ L ) ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(469,axiom,
! [A: $i,B: $i] :
( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ B @ A ) @ c_Wellfounded_Oless__than )
<=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__than__iff) ).
thf(2167,plain,
! [A: $i,B: $i] :
( ( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ B @ A ) @ c_Wellfounded_Oless__than )
=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
=> ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat @ B @ A ) @ c_Wellfounded_Oless__than ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__bot__left) ).
thf(1341,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( c_member @ D @ B @ ( c_Wellfounded_Oacc @ D @ A ) )
=> ( c_member @ D @ C @ ( c_Wellfounded_Oacc @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
thf(1674,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( c_member @ D @ B @ ( c_Wellfounded_Oacc @ D @ A ) )
=> ( c_member @ D @ C @ ( c_Wellfounded_Oacc @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(429,axiom,
c_FunDef_Oreduction__pair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ c_FunDef_Omin__strict @ c_FunDef_Omin__weak ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__rpair__set) ).
thf(2004,plain,
c_FunDef_Oreduction__pair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ tc_HOL_Obool ) @ c_FunDef_Omin__strict @ c_FunDef_Omin__weak ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(219,axiom,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__psubset__empty) ).
thf(1244,plain,
! [A: $i,B: $i] :
~ ( c_Orderings_Oord__class_Oless @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
& ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
thf(786,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
& ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A @ B ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
& ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A @ B ) )
=> ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ~ ( c_member @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equals0D) ).
thf(2152,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ~ ( c_member @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A @ B )
=> ( c_Wellfounded_OwfP @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__subset) ).
thf(1276,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A @ B )
=> ( c_Wellfounded_OwfP @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ D @ E ) )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ B @ E ) ) )
=> ( c_Wellfounded_Owf @ ( tc_prod @ A @ C ) @ ( c_Recdef_Osame__fst @ A @ C @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__same__fst) ).
thf(1590,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ D @ E ) )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ B @ E ) ) )
=> ( c_Wellfounded_Owf @ ( tc_prod @ A @ C ) @ ( c_Recdef_Osame__fst @ A @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(588,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I3_J) ).
thf(1253,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
thf(699,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Opreorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(946,plain,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
thf(1101,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ A ) @ B )
= ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff1) ).
thf(1861,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ A ) @ B )
= ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).
thf(1491,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Relation_ORange @ B @ D @ A ) )
=> ~ ! [E: $i] :
~ ( c_member @ ( tc_prod @ B @ D ) @ ( c_Product__Type_OPair @ B @ D @ E @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeE) ).
thf(1689,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Relation_ORange @ B @ D @ A ) )
=> ~ ! [E: $i] :
~ ( c_member @ ( tc_prod @ B @ D ) @ ( c_Product__Type_OPair @ B @ D @ E @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__left__commute) ).
thf(914,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Orefl__on @ D @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD) ).
thf(2041,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Orefl__on @ D @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__subset) ).
thf(1294,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(240,axiom,
! [A: $i,B: $i] : ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Wellfounded_Omeasure @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__measure) ).
thf(1308,plain,
! [A: $i,B: $i] : ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Wellfounded_Omeasure @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ ( c_Set_Oinsert @ C @ B @ A ) )
= ( c_Set_Oinsert @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(1193,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ ( c_Set_Oinsert @ C @ B @ A ) )
= ( c_Set_Oinsert @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
thf(763,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ( ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ A )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__tranclE) ).
thf(2120,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ( ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ A )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A )
=> ( c_member @ D @ B @ ( c_Relation_ORange @ E @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeI) ).
thf(2095,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A )
=> ( c_member @ D @ B @ ( c_Relation_ORange @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).
thf(2230,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(509,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B @ A ) ) )
=> ( ! [F: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ! [G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ G @ F ) @ A )
=> ( G = F ) ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).
thf(2315,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B @ A ) ) )
=> ( ! [F: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ! [G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ G @ F ) @ A )
=> ( G = F ) ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_OImage @ E @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ E @ D @ C @ A ) @ ( c_Relation_OImage @ E @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Image) ).
thf(1994,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_OImage @ E @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ E @ D @ C @ A ) @ ( c_Relation_OImage @ E @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__left__absorb) ).
thf(800,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I4_J) ).
thf(1116,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I7_J) ).
thf(620,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(291,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(1512,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Id__on) ).
thf(1280,plain,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Ototal__on @ C @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ C ) ) )
<=> ( c_Relation_Ototal__on @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__diff__Id) ).
thf(1546,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Ototal__on @ C @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ C ) ) )
=> ( c_Relation_Ototal__on @ C @ B @ A ) )
& ( ( c_Relation_Ototal__on @ C @ B @ A )
=> ( c_Relation_Ototal__on @ C @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__not__sym) ).
thf(1876,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_OImage @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__empty) ).
thf(1527,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_OImage @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
& ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__sup__iff) ).
thf(790,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
& ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
& ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_member @ G @ F @ E )
=> ( ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) @ E @ ( c_Set_Oinsert @ G @ F @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ A )
=> ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ E @ ( hAPP @ ( hAPP @ C @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).
thf(865,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_member @ G @ F @ E )
=> ( ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ G @ tc_HOL_Obool ) @ E @ ( c_Set_Oinsert @ G @ F @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ G @ tc_HOL_Obool ) ) ) ) @ A )
=> ( c_Nitpick_Ofold__graph_H @ G @ D @ C @ B @ E @ ( hAPP @ ( hAPP @ C @ F ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Relation_OId__on @ D @ A ) )
<=> ( ( C = B )
& ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__iff) ).
thf(2123,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Relation_OId__on @ D @ A ) )
=> ( ( C = B )
& ( c_member @ D @ C @ A ) ) )
& ( ( ( C = B )
& ( c_member @ D @ C @ A ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Relation_OId__on @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(494,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Ostrict__linear__order__on @ C @ B @ A )
<=> ( ( c_Relation_Otrans @ C @ A )
& ( c_Relation_Oirrefl @ C @ A )
& ( c_Relation_Ototal__on @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__linear__order__on__def) ).
thf(2258,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Order__Relation_Ostrict__linear__order__on @ C @ B @ A )
=> ( ( c_Relation_Otrans @ C @ A )
& ( c_Relation_Oirrefl @ C @ A )
& ( c_Relation_Ototal__on @ C @ B @ A ) ) )
& ( ( ( c_Relation_Otrans @ C @ A )
& ( c_Relation_Oirrefl @ C @ A )
& ( c_Relation_Ototal__on @ C @ B @ A ) )
=> ( c_Order__Relation_Ostrict__linear__order__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(950,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Relation_Oinv__image @ D @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__inv__image) ).
thf(1097,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Relation_Oinv__image @ D @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequiv @ D @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ ( c_Relation_OImage @ D @ D @ B @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__self) ).
thf(1593,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequiv @ D @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ ( c_Relation_OImage @ D @ D @ B @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Obounded__lattice__bot @ C )
=> ( ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ C ) )
<=> ( ( B
= ( c_Orderings_Obot__class_Obot @ C ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__eq__bot__iff) ).
thf(1380,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Obounded__lattice__bot @ C )
=> ( ( ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ C ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ C ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ C ) ) ) )
& ( ( ( B
= ( c_Orderings_Obot__class_Obot @ C ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ C ) ) )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev__mp) ).
thf(2008,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_member @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__subset__conv) ).
thf(1303,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(112,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__subsetI) ).
thf(867,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Relation_ODomain @ D @ B @ A ) )
<=> ? [E: $i] : ( c_member @ ( tc_prod @ D @ B ) @ ( c_Product__Type_OPair @ D @ B @ C @ E ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__iff) ).
thf(1757,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ ( c_Relation_ODomain @ D @ B @ A ) )
=> ? [E: $i] : ( c_member @ ( tc_prod @ D @ B ) @ ( c_Product__Type_OPair @ D @ B @ C @ E ) @ A ) )
& ( ? [E: $i] : ( c_member @ ( tc_prod @ D @ B ) @ ( c_Product__Type_OPair @ D @ B @ C @ E ) @ A )
=> ( c_member @ D @ C @ ( c_Relation_ODomain @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
thf(564,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( B != A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI2) ).
thf(1859,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
thf(1816,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(307,axiom,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__rtrancl) ).
thf(1561,plain,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
thf(696,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( B != A )
=> ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Diff__cancel) ).
thf(1165,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) @ ( c_Relation_ODomain @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Diff__subset) ).
thf(955,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) @ ( c_Relation_ODomain @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( c_Wellfounded_Omlex__prod @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__mlex) ).
thf(796,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( c_Wellfounded_Omlex__prod @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(143,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).
thf(960,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oleft__commute) ).
thf(635,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
=> ( c_member @ E @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD2) ).
thf(1742,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
=> ( c_member @ E @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).
thf(928,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(224,axiom,
( c_FunDef_Opair__less
= ( c_Wellfounded_Olex__prod @ tc_Nat_Onat @ tc_Nat_Onat @ c_Wellfounded_Oless__than @ c_Wellfounded_Oless__than ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__less__def) ).
thf(1261,plain,
( c_FunDef_Opair__less
= ( c_Wellfounded_Olex__prod @ tc_Nat_Onat @ tc_Nat_Onat @ c_Wellfounded_Oless__than @ c_Wellfounded_Oless__than ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(193,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Wellfounded_Omax__ext @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext__wf) ).
thf(1152,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Wellfounded_Omax__ext @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
thf(860,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( B != A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetD) ).
thf(1537,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Opartial__order__on @ C @ B @ A )
<=> ( ( c_Order__Relation_Opreorder__on @ C @ B @ A )
& ( c_Relation_Oantisym @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partial__order__on__def) ).
thf(992,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Order__Relation_Opartial__order__on @ C @ B @ A )
=> ( ( c_Order__Relation_Opreorder__on @ C @ B @ A )
& ( c_Relation_Oantisym @ C @ A ) ) )
& ( ( ( c_Order__Relation_Opreorder__on @ C @ B @ A )
& ( c_Relation_Oantisym @ C @ A ) )
=> ( c_Order__Relation_Opartial__order__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(1299,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
thf(1885,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
thf(1505,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
thf(1120,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__diff) ).
thf(1236,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) )
<=> ( ( c_Wellfounded_Owf @ D @ A )
& ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__insert) ).
thf(2241,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Owf @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) )
=> ( ( c_Wellfounded_Owf @ D @ A )
& ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) )
& ( ( ( c_Wellfounded_Owf @ D @ A )
& ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( c_Wellfounded_Owf @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__supI1) ).
thf(987,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflcl__trancl) ).
thf(1268,plain,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(17,axiom,
class_Groups_Ominus @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
thf(575,plain,
class_Groups_Ominus @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ~ ( c_member @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffD2) ).
thf(2265,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ~ ( c_member @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ A )
=> ( ( c_member @ D @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__single__insert) ).
thf(1019,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ A )
=> ( ( c_member @ D @ B @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(316,axiom,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__empty) ).
thf(1597,plain,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclE) ).
thf(1880,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ ( c_Product__Type_OPair @ D @ C @ B @ A ) ) )
=> ( hBOOL @ ( c_Product__Type_Ocurry @ D @ C @ tc_HOL_Obool @ E @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryI) ).
thf(1902,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ ( c_Product__Type_OPair @ D @ C @ B @ A ) ) )
=> ( hBOOL @ ( c_Product__Type_Ocurry @ D @ C @ tc_HOL_Obool @ E @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
thf(691,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oorder @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
thf(1331,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Oorder @ C )
=> ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( B != A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
& ( B != A ) )
=> ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(803,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) )
=> ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ D @ C )
=> ( ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ B @ D ) @ c_FunDef_Opair__leq )
=> ( ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ A @ C ) @ c_FunDef_Omax__weak )
=> ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ B @ A ) @ C ) @ c_FunDef_Omax__weak ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wmax__insertI) ).
thf(1944,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ D @ C )
=> ( ( c_member @ ( tc_prod @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ B @ D ) @ c_FunDef_Opair__leq )
=> ( ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ A @ C ) @ c_FunDef_Omax__weak )
=> ( c_member @ ( tc_prod @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OPair @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ ( tc_prod @ tc_Nat_Onat @ tc_Nat_Onat ) @ B @ A ) @ C ) @ c_FunDef_Omax__weak ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(414,axiom,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Id__on) ).
thf(1962,plain,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__insert__right) ).
thf(1009,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ E @ D @ C ) @ B ) @ A ) )
<=> ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rel__def) ).
thf(1737,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ E @ D @ C ) @ B ) @ A ) )
=> ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ B @ A ) @ C ) )
& ( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ B @ A ) @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ E @ D @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(205,axiom,
! [A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__empty) ).
thf(1184,plain,
! [A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Relation_ORange @ B @ D @ A ) )
<=> ? [E: $i] : ( c_member @ ( tc_prod @ B @ D ) @ ( c_Product__Type_OPair @ B @ D @ E @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__iff) ).
thf(1565,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ ( c_Relation_ORange @ B @ D @ A ) )
=> ? [E: $i] : ( c_member @ ( tc_prod @ B @ D ) @ ( c_Product__Type_OPair @ B @ D @ E @ C ) @ A ) )
& ( ? [E: $i] : ( c_member @ ( tc_prod @ B @ D ) @ ( c_Product__Type_OPair @ B @ D @ E @ C ) @ A )
=> ( c_member @ D @ C @ ( c_Relation_ORange @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oleft__idem) ).
thf(543,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__mono) ).
thf(1848,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__r__diff__Id) ).
thf(1037,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__subset) ).
thf(755,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(173,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(1088,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
| ( B = A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(455,axiom,
! [A: $i,B: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ A @ ( c_Relation_OId @ B ) )
=> ~ ! [C: $i] :
( A
!= ( c_Product__Type_OPair @ B @ B @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IdE) ).
thf(2106,plain,
! [A: $i,B: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ A @ ( c_Relation_OId @ B ) )
=> ~ ! [C: $i] :
( A
!= ( c_Product__Type_OPair @ B @ B @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(118,axiom,
! [A: $i] : ( c_Relation_Osingle__valued @ A @ A @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__Id) ).
thf(882,plain,
! [A: $i] : ( c_Relation_Osingle__valued @ A @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ A ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__mono) ).
thf(1417,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ A ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).
thf(1204,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Nitpick_Ofold__graph_H @ D @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(369,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ D ) @ A )
=> ! [E: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ E ) @ A )
=> ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ E ) @ A ) ) )
=> ( c_Relation_Otrans @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transI) ).
thf(1812,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ D ) @ A )
=> ! [E: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ E ) @ A )
=> ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ E ) @ A ) ) )
=> ( c_Relation_Otrans @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(2409,plain,
$false,
inference(cvc4,[status(thm)],[645,1322,1024,1823,1559,1729,1899,1850,555,1168,760,2131,1454,1083,962,1982,666,1818,2363,1005,2117,683,730,1443,1401,1939,741,2099,655,597,1173,1971,1533,614,1692,677,1608,1310,550,1735,2184,814,1988,747,1458,670,1078,1788,1507,2360,1196,1835,1782,1441,973,1613,1724,2067,1887,651,2227,1391,2010,1935,1650,1645,2136,1904,1518,1703,1628,1709,2328,570,1430,2039,1660,2339,1871,2217,917,1313,1832,1992,1132,724,1055,1409,638,1247,1319,1347,2158,1773,1778,2222,1415,924,1946,2027,2090,1373,1911,623,1864,1828,937,1283,821,905,1040,1632,2291,2254,1581,2335,687,1377,2281,877,734,1622,1433,1600,1242,1521,1696,1975,2002,998,1074,1206,942,2204,1438,546,1338,2047,2093,2000,1199,2164,2232,2296,798,1163,957,1255,1217,1502,561,693,2249,1021,1570,1676,1365,1920,1951,1296,1687,1624,1159,1210,757,1634,842,1012,1938,847,1032,1602,522,830,889,2179,2313,1128,2112,1291,1541,874,1762,948,1953,1804,725,1878,593,869,610,989,1397,2300,578,783,1118,1493,884,1964,933,669,642,1842,1700,2349,1744,706,1419,554,753,1791,2172,590,2085,837,1263,701,1266,1974,1932,1050,1825,1324,1114,1588,1099,1451,738,1530,1539,1456,1202,2043,921,1563,1187,1663,1515,1026,662,926,765,1846,2076,1170,1286,1035,1466,558,794,586,2235,1146,2149,824,1273,1747,1927,1595,573,689,601,1278,1906,750,1510,1698,1959,1103,819,562,1007,1620,1752,2016,1388,1535,1403,1795,1124,1488,584,1154,641,2293,611,713,1464,1271,2308,1058,1107,1239,1997,900,2151,1894,1806,1524,567,1144,599,1349,2097,880,649,616,1122,2197,1969,863,2065,1175,890,2182,1080,631,816,1630,2267,1909,848,1029,1344,1460,2252,1177,1821,594,1149,964,685,2212,1445,780,1015,563,2022,2101,2303,2156,2207,1694,2069,768,827,1775,1435,1726,1250,2005,1626,722,2239,675,944,2271,2037,1134,939,2256,1551,1990,2202,2298,872,1156,887,1647,1368,1780,2060,707,1869,2337,2276,1830,1130,643,1220,2354,840,1785,576,1658,2322,2247,744,703,1141,2357,727,1797,1485,2320,1052,845,1421,627,2045,1180,931,1553,671,1913,581,2209,2110,771,1966,556,2310,1844,688,903,2347,1412,1448,2187,1866,2071,2167,1341,1674,2004,1244,786,2152,1276,1590,588,1253,699,946,1101,1861,1491,1689,914,2041,1294,1308,1193,763,2120,2095,2230,2315,1994,800,1116,620,1512,1280,1546,1876,1527,790,865,2123,2258,950,1097,1593,1380,2008,1303,867,1757,564,1859,1816,1561,696,1165,955,796,960,635,1742,928,1261,1152,860,1537,992,1299,1885,1505,1120,1236,2241,987,1268,575,2265,1019,1597,1880,1902,691,1331,803,1944,1962,1009,1737,1184,1565,543,1848,1037,755,1088,2106,882,1417,1204,1812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SCT105+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 15:26:18 EDT 2023
% 0.15/0.36 % CPUTime :
% 1.00/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.65/1.14 % [INFO] Parsing done (249ms).
% 1.65/1.15 % [INFO] Running in sequential loop mode.
% 2.37/1.35 % [INFO] eprover registered as external prover.
% 2.37/1.35 % [INFO] cvc4 registered as external prover.
% 2.37/1.35 % [INFO] Scanning for conjecture ...
% 2.88/1.47 % [INFO] Found a conjecture and 522 axioms. Running axiom selection ...
% 3.14/1.60 % [INFO] Axiom selection finished. Selected 519 axioms (removed 3 axioms).
% 4.14/1.86 % [INFO] Problem is first-order (TPTP FOF).
% 4.14/1.88 % [INFO] Type checking passed.
% 4.14/1.88 % [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 ...
% 17.87/5.08 % External prover 'cvc4' found a proof!
% 17.87/5.08 % [INFO] Killing All external provers ...
% 17.87/5.08 % Time passed: 4574ms (effective reasoning time: 3931ms)
% 17.87/5.08 % 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)>
% 17.87/5.09 % Axioms used in derivation (519): fact_wf__not__refl, fact_order__le__neq__trans, fact_wmax__insertI, fact_transI, fact_wfrec__rel_Ointros, fact_single__valued__Id__on, fact_insertCI, fact_ImageE, fact_wf__not__sym, fact_refl__onD2, fact_wf__inv__image, fact_acc__wfI, fact_Field__empty, fact_Un__absorb1, fact_xt1_I1_J, fact_converse__rtrancl__induct2, fact_singleton__iff, fact_wmin__emptyI, fact_Diff__insert__absorb, arity_fun__Orderings_Oorder, fact_cut__apply, fact_sup1I1, fact_order__le__less__trans, fact_pair__lessI2, fact_smax__insertI, fact_insert__iff, arity_Nat__Onat__Lattices_Olattice, fact_le__eq__less__or__eq, fact_nat__less__cases, fact_diff__le__mono2, fact_xt1_I4_J, fact_UnI1, fact_termination__basic__simps_I5_J, fact_insert__subset, fact_rtranclD, arity_Nat__Onat__Orderings_Oorder, fact_pred__nat__trancl__eq__le, fact_sup__apply, fact_Un__mono, fact_Transitive__Closure_Otrancl__into__trancl, fact_wmin__insertI, fact_curry__conv, fact_IdI, fact_insertI1, fact_order__less__asym_H, fact_Un__empty__left, fact_less__imp__le__nat, fact_less__supI1, fact_bot__apply, fact_prod_Orecs, fact_union__comp__emptyR, fact_trancl__id, fact_mono__Field, fact_min__ext__wf, fact_linorder__not__le, fact_linorder__antisym__conv2, fact_acc_Osimps, fact_diff__diff__cancel, arity_HOL__Obool__Orderings_Opreorder, fact_linorder__neqE, fact_sup__assoc, fact_curryE, fact_leI, fact_empty__not__insert, fact_trans__Id__on, fact_rtrancl__empty, fact_order__eq__refl, fact_Un__insert__left, arity_fun__Lattices_Olattice, fact_max__ext__additive, fact_rtrancl_Ortrancl__refl, fact_r__into__trancl_H, fact_rel__compI, help_c__fequal__2, fact_converse__rtrancl__induct, fact_min__strict__def, fact_acyclic__impl__antisym__rtrancl, fact_le__neq__implies__less, fact_tranclD2, fact_linorder__antisym__conv3, fact_order__less__imp__not__eq, fact_max__rpair__set, fact_pair__leq__def, fact_rtrancl__mono, fact_rtrancl__subset__rtrancl, fact_insert__not__empty, fact_converse__rtranclE2, fact_split__paired__All, fact_Diff__subset, fact_sup__absorb1, fact_equalityD2, fact_antisymI, fact_Field__Un, fact_less__eq, fact_Range__empty, fact_rev__ImageI, fact_linorder__antisym__conv1, fact_tranclE, fact_acc_OaccI, fact_le__supI, fact_le__supI2, fact_single__valued__Id, fact_predicate2D, fact_Diff__idemp, fact_diff__le__self, fact_singleton__inject, fact_le__funD, fact_emptyE, fact_le__fun__def, fact_acc__subset, fact_DiffD2, fact_reduction__pairI, fact_sup__ge2, fact_wf__irrefl, fact_linorder__less__linear, fact_Image__Un, fact_order__less__imp__not__less, fact_lnear__order__on__empty, fact_DiffE, fact_Domain__empty__iff, fact_ord__less__eq__trans, fact_in__mono, fact_Domain__Un__eq, fact_wf__lex__prod, fact_wf__measure, fact_diff__commute, fact_xt1_I9_J, fact_Diff__subset__conv, fact_sup__least, fact_rtrancl__unfold, fact_in__measure, fact_minus__apply, fact_rtrancl__subset, fact_max__weak__def, fact_subset__singletonD, fact_sup__eq__bot__iff, fact_single__valued__subset, fact_insert__is__Un, fact_less__or__eq__imp__le, arity_HOL__Obool__Lattices_Olattice, fact_wfE__pf, fact_subset__iff__psubset__eq, fact_Id__on__iff, fact_Diff__insert, fact_tfl__cut__apply, fact_fold__graph_H_Oequations_I1_J, fact_wf__subset, fact_rtrancl__Un__separator__converseE, fact_Domain__insert, fact_rtrancl__reflcl, arity_Nat__Onat__Orderings_Opreorder, fact_antisym__empty, fact_order__less__imp__not__eq2, fact_order__antisym, fact_xt1_I10_J, fact_less__irrefl__nat, fact_refl__onD, fact_sup__bot__left, fact_order__refl, arity_fun__Lattices_Osemilattice__sup, fact_acc__downwards, fact_Un__left__commute, fact_sup1I2, fact_Un__empty, fact_Domain__mono, fact_preorder__on__def, arity_HOL__Obool__Lattices_Osemilattice__sup, fact_xt1_I5_J, fact_insert__code, fact_Domain__empty, fact_wf__empty, fact_bot__least, fact_subset__Image1__Image1__iff, fact_insert__Diff__single, fact_Domain__Diff__subset, fact_refl__on__empty, arity_Nat__Onat__Groups_Ominus, fact_trans__inv__image, fact_rtrancl__Un__separatorE, fact_rtrancl__Un__rtrancl, fact_RangeI, arity_HOL__Obool__Groups_Ominus, fact_nat__neq__iff, fact_rtrancl__reflcl__absorb, fact_DomainI, fact_Diff__empty, fact_ex__in__conv, fact_sup__left__commute, arity_Nat__Onat__Lattices_Osemilattice__sup, fact_subset__insertI, fact_notin__Lin__iff, fact_xt1_I3_J, fact_wf__pred__nat, fact_less__imp__neq, fact_xt1_I8_J, fact_predicate1D, fact_less__not__refl3, fact_eq__mem, fact_trans__diff__Id, fact_smin__insertI, arity_HOL__Obool__Orderings_Oord, fact_Diff__partition, fact_Id__onE, fact_RangeE, fact_sup__left__idem, fact_insert__absorb2, fact_le__supI1, fact_converse__rtranclE, fact_equals0D, fact_insert__absorb, fact_subset__insert, fact_Un__Image, fact_pair__in__Id__conv, fact_max__ext__wf, fact_insertI2, fact_Diff__cancel, fact_same__fstI, fact_trans__Id, fact_trancl__trans, fact_equalityD1, fact_trans__def, fact_Refl__antisym__eq__Image1__Image1__iff, fact_diff__single__insert, fact_le__funE, fact_wfrec, fact_eqset__imp__iff, fact_trancl__empty, fact_in__rtrancl__UnI, fact_order__neq__le__trans, fact_converse__rtrancl__into__rtrancl, fact_Un__insert__right, arity_fun__Orderings_Opreorder, fact_rtrancl__trans, fact_less__by__empty, fact_less__imp__diff__less, help_c__fequal__1, fact_refl__on__Un, fact_linorder__neq__iff, fact_DiffD1, arity_Nat__Onat__Orderings_Oord, fact_irrefl__def, fact_UnI2, fact_rp__inv__image__rp, fact_insert__commute, fact_subset__Un__eq, fact_le__iff__sup, fact_sup_Oassoc, fact_ord__le__eq__trans, fact_antisym__subset, fact_all__not__in__conv, fact_mlex__leq, fact_set__mp, fact_less__than__iff, fact_linorder__neqE__nat, fact_Image__singleton__iff, fact_not__less__iff__gr__or__eq, fact_Un__Diff__cancel, fact_wfrec__rel_Oequations, fact_r__r__into__trancl, fact_def__wfrec, fact_subset__equiv__class, fact_total__on__def, fact_irrefl__trancl__rD, fact_Diff__mono, fact_psubsetD, fact_fold__graph_H_Ointros_I1_J, fact_bex__Un, fact_partial__order__on__def, fact_Range__Id__on, fact_reflcl__trancl, fact_inf__sup__aci_I8_J, fact_antisym__def, fact_Range__iff, fact_sup1CI, fact_Image__empty, fact_rtrancl__into__trancl2, fact_Nitpick_Orefl_H__def, fact_trans__reflclI, fact_psubset__trans, fact_double__diff, fact_order__less__le, fact_sup__ge1, fact_wf__acc__iff, arity_Nat__Onat__Orderings_Obot, fact_set__eq__subset, fact_acyclic__insert, fact_partial__order__on__empty, fact_Pair__inject, fact_xt1_I12_J, fact_linear__order__on__def, fact_subset__refl, fact_fold__graph_H_Ointros_I2_J, fact_internal__split__conv, fact_single__valued__confluent, arity_fun__Orderings_Oord, fact_equalityI, fact_ext, fact_order__less__not__sym, fact_le__supE, fact_smin__emptyI, fact_acc__wfD, fact_eq__diff__iff, arity_HOL__Obool__Orderings_Oorder, fact_linorder__le__less__linear, arity_fun__Orderings_Obot, fact_empty__iff, fact_wf__in__rel, fact_Image__closed__trancl, fact_sup__idem, fact_less__le__not__le, arity_Nat__Onat__Orderings_Olinorder, fact_rtrancl__induct2, fact_rtrancl__trancl__absorb, fact_nat__le__linear, fact_linorder__le__cases, fact_Id__on__eqI, fact_trancl__range, fact_acyclic__def, fact_order__less__le__trans, fact_max__strict__def, fact_rtrancl__eq__or__trancl, fact_refl__onD1, fact_not__leE, fact_leD, fact_total__on__empty, fact_insert__ident, fact_subset__Image__Image__iff, fact_acyclic__subset, fact_curryD, fact_subset__empty, fact_singletonE, fact_diff__less__mono2, fact_subset__insert__iff, fact_trancl__into__rtrancl, fact_rtrancl__Un__subset, fact_diff__eq__diff__less, fact_sup__mono, fact_Range__Diff__subset, fact_converse__tranclE, fact_rtrancl__r__diff__Id, fact_sup_Oidem, fact_preorder__on__empty, fact_wf__eq__minimal, arity_HOL__Obool__Lattices_Obounded__lattice__bot, fact_order__less__asym, fact_mlex__less, fact_psubset__imp__subset, fact_less__than__def, fact_Un__absorb, fact_trancl_Or__into__trancl, fact_min__rpair__set, fact_set__rev__mp, fact_tranclD, fact_Domain__iff, fact_DiffI, fact_pair__less__def, fact_eq__mem__trans, fact_antisymD, fact_trans__lex__prod, fact_acc__downwards__aux, fact_Un__empty__right, fact_wf__insert, fact_diff__less__mono, fact_rtrancl__induct, fact_sup__commute, fact_trancl__rtrancl__absorb, fact_rev__predicate2D, fact_linorder__linear, fact_total__on__diff__Id, fact_transD, fact_trancl__into__trancl2, fact_single__valuedI, fact_subset__insertI2, fact_Un__absorb2, fact_less__not__refl2, fact_single__valued__def, fact_DomainE, fact_xt1_I6_J, fact_Nat_Odiff__diff__eq, fact_le__refl, fact_antisym__reflcl, fact_strict__linear__order__on__diff__Id, fact_in__lex__prod, fact_strict__linear__order__on__def, fact_inf__sup__aci_I5_J, fact_ball__Un, fact_Un__upper1, fact_xt1_I2_J, fact_UnCI, fact_linorder__not__less, fact_less__fun__def, fact_rev__predicate1D, fact_insert__Diff, fact_trans__rtrancl, fact_Domain__Id__on, fact_cuts__eq, fact_wf__trancl, fact_pair__leqI1, fact_equalityE, fact_Pair__eq, fact_tfl__wfrec, fact_in__rel__def, fact_inf__sup__ord_I4_J, fact_le__sup__iff, fact_subset__psubset__trans, fact_irrefl__diff__Id, fact_IdE, fact_measure__def, fact_order__eq__iff, fact_rtrancl_Ortrancl__into__rtrancl, fact_rtranclE, fact_empty__subsetI, fact_insert__Diff__if, fact_less__not__refl, fact_insert__mono, fact_ord__eq__less__trans, fact_sup_Ocommute, fact_Un__Diff__cancel2, fact_Range__Un__eq, fact_wf__mlex, arity_fun__Groups_Ominus, fact_Nitpick_Owf__wfrec_H__def, fact_le__trans, fact_less__supI2, fact_equalityCE, fact_r__into__rtrancl, fact_psubset__insert__iff, fact_rtrancl__into__trancl1, fact_Un__iff, fact_Not__Domain__rtrancl, fact_rtrancl__idemp, fact_Diff__insert2, fact_subsetD, fact_Un__Diff, fact_psubset__eq, fact_trancl__rtrancl__trancl, fact_sup1E, fact_inf__sup__aci_I7_J, fact_inf__sup__ord_I3_J, fact_wf__same__fst, fact_diff__eq__diff__less__eq, fact_Id__on__empty, fact_Range__insert, fact_in__inv__image, fact_the__elem__eq, fact_insertE, fact_empty__Diff, fact_trans__less__than, fact_acyclicI, fact_acc__downward, fact_Range__empty__iff, fact_inf__sup__aci_I6_J, fact_eq__imp__le, fact_diff__eq__diff__eq, fact_order__le__imp__less__or__eq, fact_antisym__Id__on, fact_order__antisym__conv, fact_le__antisym, fact_Un__commute, fact_eqelem__imp__iff, arity_HOL__Obool__Orderings_Obot, fact_Image__iff, fact_diff__le__mono, fact_sup__bot__right, fact_pair__lessI1, fact_psubset__subset__trans, fact_Un__least, fact_curryI, fact_well__order__on__def, fact_wf__acyclic, fact_subset__trans, fact_sup__absorb2, fact_min__weak__def, fact_Diff__iff, fact_order__less__imp__le, fact_order__less__trans, fact_pair__leqI2, fact_trans__trancl, fact_Un__upper2, fact_antisym__Id, fact_order__less__irrefl, fact_Partial__order__eq__Image1__Image1__iff, fact_Un__left__absorb, fact_order__le__less, fact_sup_Oleft__idem, fact_le__diff__iff, fact_wf__asym, fact_not__psubset__empty, fact_mem__def, fact_refl__on__Id__on, fact_wfrec__rel_Osimps, fact_nat__less__le, fact_wf__pair__less, fact_trancl__mono, fact_ord__eq__le__trans, fact_fold__graph_H_Oequations_I2_J, fact_Field__insert, fact_less__diff__iff, fact_sup_Oleft__commute, fact_linorder__cases, fact_xt1_I11_J, fact_UnE, fact_equiv__class__self, fact_wf__less__than, fact_Image__mono, fact_wfP__subset, fact_rtrancl__trancl__trancl, fact_not__acc__down, fact_doubleton__eq__iff, fact_order__trans, fact_trancl__reflcl, fact_Field__def, fact_Image__Id, fact_trancl__domain, fact_Un__assoc, fact_single__valuedD, fact_well__order__on__empty, fact_insert__Diff1, fact_xt1_I7_J
% 17.87/5.09 % No. of inferences in proof: 1042
% 17.87/5.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4574 ms resp. 3931 ms w/o parsing
% 18.75/5.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.75/5.32 % [INFO] Killing All external provers ...
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