TSTP Solution File: SCT115+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT115+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 11:50:35 EDT 2023
% Result : Theorem 19.04s 5.08s
% Output : Refutation 19.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 607
% Syntax : Number of formulae : 1134 ( 267 unt; 82 typ; 0 def)
% Number of atoms : 3086 ( 714 equ; 0 cnn)
% Maximal formula atoms : 47 ( 2 avg)
% Number of connectives : 19496 ( 377 ~; 93 |; 366 &;17085 @)
% ( 111 <=>;1464 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 191 ( 191 >; 0 *; 0 +; 0 <<)
% Number of symbols : 84 ( 82 usr; 10 con; 0-6 aty)
% Number of variables : 3726 ( 0 ^;3678 !; 48 ?;3726 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_member_type,type,
c_member: $i > $i > $i > $o ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i > $i > $i ).
thf(v_L_type,type,
v_L: $i ).
thf(v_x_type,type,
v_x: $i ).
thf(v_y_type,type,
v_y: $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_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(class_Groups_Ominus_type,type,
class_Groups_Ominus: $i > $o ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(class_Lattices_Osemilattice__inf_type,type,
class_Lattices_Osemilattice__inf: $i > $o ).
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(hAPP_type,type,
hAPP: $i > $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(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_Relation_Otrans_type,type,
c_Relation_Otrans: $i > $i > $o ).
thf(c_Lattices_Osemilattice__inf__class_Oinf_type,type,
c_Lattices_Osemilattice__inf__class_Oinf: $i > $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_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_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_Wellfounded_Opred__nat_type,type,
c_Wellfounded_Opred__nat: $i ).
thf(c_Relation_OField_type,type,
c_Relation_OField: $i > $i > $i ).
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_Relation_Ototal__on_type,type,
c_Relation_Ototal__on: $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_Relation_Orefl__on_type,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
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(c_Nitpick_Ofold__graph_H_type,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Order__Relation_Olinear__order__on_type,type,
c_Order__Relation_Olinear__order__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_Set_Othe__elem_type,type,
c_Set_Othe__elem: $i > $i > $i ).
thf(c_Wellfounded_OwfP_type,type,
c_Wellfounded_OwfP: $i > $i > $o ).
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_Oin__rel_type,type,
c_FunDef_Oin__rel: $i > $i > $i > $i ).
thf(c_Order__Relation_Ostrict__linear__order__on_type,type,
c_Order__Relation_Ostrict__linear__order__on: $i > $i > $i > $o ).
thf(c_Relation_Oirrefl_type,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(c_Arrow__Order__Mirabelle_OLin_type,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(c_Arrow__Order__Mirabelle_Omktop_type,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omkbot_type,type,
c_Arrow__Order__Mirabelle_Omkbot: $i > $i > $i ).
thf(c_Product__Type_OSigma_type,type,
c_Product__Type_OSigma: $i > $i > $i > $i > $i ).
thf(c_Recdef_Osame__fst_type,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
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_Arrow__Order__Mirabelle_Oabove_type,type,
c_Arrow__Order__Mirabelle_Oabove: $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_Ocurry_type,type,
c_Product__Type_Ocurry: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Product__Type_Oprod_Oprod__rec_type,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Wellfounded_Olex__prod_type,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Obelow_type,type,
c_Arrow__Order__Mirabelle_Obelow: $i > $i > $i > $i ).
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_Equiv__Relations_Oequiv_type,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
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(645,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(442,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(2199,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)],[442]) ).
thf(150,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(1036,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)],[150]) ).
thf(254,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(1411,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)],[254]) ).
thf(195,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(1190,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)],[195]) ).
thf(469,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(2306,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)],[469]) ).
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 ) @ ( 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(2072,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)],[410]) ).
thf(169,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(1105,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)],[169]) ).
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(909,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(501,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(2463,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)],[501]) ).
thf(226,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(1315,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)],[226]) ).
thf(126,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(941,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)],[126]) ).
thf(69,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(777,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)],[69]) ).
thf(354,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(1818,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)],[354]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oconverse @ D @ D @ ( hAPP @ ( c_Relation_Oinv__image @ C @ D @ B ) @ A ) )
= ( hAPP @ ( c_Relation_Oinv__image @ C @ D @ ( c_Relation_Oconverse @ C @ C @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__inv__image) ).
thf(1501,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oconverse @ D @ D @ ( hAPP @ ( c_Relation_Oinv__image @ C @ D @ B ) @ A ) )
= ( hAPP @ ( c_Relation_Oinv__image @ C @ D @ ( c_Relation_Oconverse @ C @ C @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(498,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(2452,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)],[498]) ).
thf(82,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(809,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)],[82]) ).
thf(476,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(2336,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)],[476]) ).
thf(419,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(2109,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)],[419]) ).
thf(426,axiom,
( ! [A: $i,B: $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 @ B ) @ v_L )
=> ! [C: $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 @ B @ C ) @ 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 @ C ) @ 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_1) ).
thf(2131,plain,
( ! [A: $i,B: $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 @ B ) @ v_L )
=> ! [C: $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 @ B @ C ) @ 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 @ C ) @ 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(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(401,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(2031,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)],[401]) ).
thf(487,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(2412,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)],[487]) ).
thf(204,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(1237,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)],[204]) ).
thf(190,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(1179,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)],[190]) ).
thf(474,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(2331,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)],[474]) ).
thf(378,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(1956,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)],[378]) ).
thf(376,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(1950,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)],[376]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
thf(1554,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(171,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(1110,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)],[171]) ).
thf(137,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(977,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)],[137]) ).
thf(417,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(2104,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)],[417]) ).
thf(38,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(683,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)],[38]) ).
thf(351,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(1808,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)],[351]) ).
thf(520,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(2527,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)],[520]) ).
thf(54,axiom,
class_Orderings_Obot @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
thf(741,plain,
class_Orderings_Obot @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(480,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(2380,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)],[480]) ).
thf(383,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(1971,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)],[383]) ).
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(597,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(260,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
= ( c_Relation_Oconverse @ B @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converse) ).
thf(1437,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
= ( c_Relation_Oconverse @ B @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(256,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(1422,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)],[256]) ).
thf(297,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(1569,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)],[297]) ).
thf(152,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(1041,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)],[152]) ).
thf(100,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(861,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)],[100]) ).
thf(318,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(1655,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)],[318]) ).
thf(500,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(2459,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)],[500]) ).
thf(127,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(945,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)],[127]) ).
thf(279,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(1507,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)],[279]) ).
thf(337,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(1756,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)],[337]) ).
thf(224,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(1310,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)],[224]) ).
thf(84,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(814,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)],[84]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ E @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ E @ C @ B ) @ ( c_Relation_OImage @ D @ E @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Int__subset) ).
thf(1327,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ E @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ E @ C @ B ) @ ( c_Relation_OImage @ D @ E @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(505,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(2476,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)],[505]) ).
thf(213,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(1260,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)],[213]) ).
thf(237,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(1342,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)],[237]) ).
thf(57,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(747,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)],[57]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ F @ E @ D )
=> ( ( c_member @ C @ B @ ( hAPP @ A @ E ) )
=> ( c_member @ ( tc_prod @ F @ C ) @ ( c_Product__Type_OPair @ F @ C @ E @ B ) @ ( c_Product__Type_OSigma @ F @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaI) ).
thf(2227,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ F @ E @ D )
=> ( ( c_member @ C @ B @ ( hAPP @ A @ E ) )
=> ( c_member @ ( tc_prod @ F @ C ) @ ( c_Product__Type_OPair @ F @ C @ E @ B ) @ ( c_Product__Type_OSigma @ F @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(72,axiom,
class_Lattices_Osemilattice__sup @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
thf(782,plain,
class_Lattices_Osemilattice__sup @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
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(2020,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(313,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(1613,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)],[313]) ).
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(2010,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(409,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(2067,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)],[409]) ).
thf(283,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(1518,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)],[283]) ).
thf(202,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(1228,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)],[202]) ).
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(651,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(510,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(2491,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)],[510]) ).
thf(526,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(2548,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)],[526]) ).
thf(341,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(1782,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)],[341]) ).
thf(309,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(1601,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)],[309]) ).
thf(250,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(1386,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)],[250]) ).
thf(51,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(724,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)],[51]) ).
thf(344,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(1792,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)],[344]) ).
thf(386,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(1985,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)],[386]) ).
thf(74,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(785,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)],[74]) ).
thf(225,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
=> ( c_Wellfounded_Owf @ B @ ( c_Relation_Oconverse @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__converse__trancl) ).
thf(1313,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
=> ( c_Wellfounded_Owf @ B @ ( c_Relation_Oconverse @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(300,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(1577,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)],[300]) ).
thf(389,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(1992,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)],[389]) ).
thf(424,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(2126,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)],[424]) ).
thf(496,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(2444,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)],[496]) ).
thf(214,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(1264,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)],[214]) ).
thf(445,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(2217,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)],[445]) ).
thf(229,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(1323,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)],[229]) ).
thf(11,axiom,
class_Lattices_Olattice @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
thf(619,plain,
class_Lattices_Olattice @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(91,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(838,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)],[91]) ).
thf(117,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(917,plain,
! [A: $i,B: $i] :
( ( c_Relation_OImage @ B @ B @ ( c_Relation_OId @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Osemilattice__inf @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
thf(751,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Osemilattice__inf @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(266,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(1462,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)],[266]) ).
thf(157,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(1059,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)],[157]) ).
thf(490,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(2420,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)],[490]) ).
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(638,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(249,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(1379,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)],[249]) ).
thf(436,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(2169,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)],[436]) ).
thf(208,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(1247,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)],[208]) ).
thf(362,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(1890,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)],[362]) ).
thf(272,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(1479,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)],[272]) ).
thf(146,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(1013,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)],[146]) ).
thf(335,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(1741,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)],[335]) ).
thf(433,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(2158,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)],[433]) ).
thf(381,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 ) @ ( c_Relation_Oconverse @ D @ E @ A ) )
<=> ( c_member @ ( tc_prod @ D @ E ) @ ( c_Product__Type_OPair @ D @ E @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__iff) ).
thf(1963,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 ) @ ( c_Relation_Oconverse @ D @ E @ A ) )
=> ( c_member @ ( tc_prod @ D @ E ) @ ( c_Product__Type_OPair @ D @ E @ B @ C ) @ A ) )
& ( ( c_member @ ( tc_prod @ D @ E ) @ ( c_Product__Type_OPair @ D @ E @ B @ C ) @ A )
=> ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(482,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(2388,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)],[482]) ).
thf(167,axiom,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__Id) ).
thf(1100,plain,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(85,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(817,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)],[85]) ).
thf(111,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(902,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)],[111]) ).
thf(135,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(969,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)],[135]) ).
thf(7,axiom,
class_Orderings_Oord @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(606,plain,
class_Orderings_Oord @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(451,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(2237,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)],[451]) ).
thf(120,axiom,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Oless__than,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__less__than) ).
thf(924,plain,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Oless__than,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(223,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(1302,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)],[223]) ).
thf(456,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(2259,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)],[456]) ).
thf(380,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(1960,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)],[380]) ).
thf(221,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(1283,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)],[221]) ).
thf(375,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(1946,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)],[375]) ).
thf(267,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(1465,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)],[267]) ).
thf(352,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 @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( c_Relation_Oconverse @ D @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converseI) ).
thf(1811,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 @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( c_Relation_Oconverse @ D @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(263,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(1450,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)],[263]) ).
thf(523,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(2540,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)],[523]) ).
thf(402,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(2034,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)],[402]) ).
thf(186,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(1169,plain,
( c_Wellfounded_Oless__than
= ( c_Transitive__Closure_Otrancl @ tc_Nat_Onat @ c_Wellfounded_Opred__nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(248,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(1377,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)],[248]) ).
thf(463,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 @ ( c_Relation_Oconverse @ D @ 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_rtrancl__converseD) ).
thf(2281,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 @ ( c_Relation_Oconverse @ D @ D @ A ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(508,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(2483,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)],[508]) ).
thf(492,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 @ ( c_Relation_Oconverse @ D @ D @ A ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ D @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converseD) ).
thf(2424,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 @ ( c_Relation_Oconverse @ D @ D @ A ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ D @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
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(660,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(206,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(1242,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)],[206]) ).
thf(1,conjecture,
( ! [A: $i,B: $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 @ B ) @ v_L )
& ( A != v_x )
& ( B != v_x ) )
=> ! [C: $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 @ B @ C ) @ v_L )
& ( C != v_x ) )
=> ( 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 @ C ) @ v_L ) )
& ( ( ( C = v_x )
& ( 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 @ v_y ) @ 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 @ v_y ) @ v_L ) ) ) )
& ( ( ( B = v_x )
& ( 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 @ v_y ) @ v_L )
& ( A != v_x ) )
=> ! [C: $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 @ v_y @ C ) @ v_L )
& ( C != v_x ) )
=> ( 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 @ C ) @ v_L ) ) )
& ( ( ( A = v_x )
& ( 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 @ v_y @ B ) @ v_L )
& ( B != v_x ) )
=> ! [C: $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 @ B @ C ) @ v_L )
& ( C != v_x ) )
=> ( ( C = v_y )
| ( 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 @ v_y @ C ) @ v_L ) ) )
& ( ( C = v_x )
=> ~ ( 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 @ v_y ) @ v_L ) ) ) ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( ( A = v_x )
& ( B = v_y ) )
| ( ( 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 )
& ( A != v_x )
& ( B != v_x ) )
| ( ( B = v_x )
& ( 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 @ v_y ) @ v_L )
& ( A != v_x ) )
| ( ( A = v_x )
& ( 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 @ v_y @ B ) @ v_L )
& ( B != v_x ) )
| ( ( B = v_x )
& ( A = v_y ) )
| ( ( 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 )
& ( B != v_x )
& ( A != v_x ) )
| ( ( A = v_x )
& ( 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 @ v_y ) @ v_L )
& ( B != v_x ) )
| ( ( B = v_x )
& ( 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 @ v_y @ A ) @ v_L )
& ( A != v_x ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: $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 @ B ) @ v_L )
& ( A != v_x )
& ( B != v_x ) )
=> ! [C: $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 @ B @ C ) @ v_L )
& ( C != v_x ) )
=> ( 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 @ C ) @ v_L ) )
& ( ( ( C = v_x )
& ( 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 @ v_y ) @ 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 @ v_y ) @ v_L ) ) ) )
& ( ( ( B = v_x )
& ( 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 @ v_y ) @ v_L )
& ( A != v_x ) )
=> ! [C: $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 @ v_y @ C ) @ v_L )
& ( C != v_x ) )
=> ( 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 @ C ) @ v_L ) ) )
& ( ( ( A = v_x )
& ( 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 @ v_y @ B ) @ v_L )
& ( B != v_x ) )
=> ! [C: $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 @ B @ C ) @ v_L )
& ( C != v_x ) )
=> ( ( C = v_y )
| ( 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 @ v_y @ C ) @ v_L ) ) )
& ( ( C = v_x )
=> ~ ( 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 @ v_y ) @ v_L ) ) ) ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( ( A = v_x )
& ( B = v_y ) )
| ( ( 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 )
& ( A != v_x )
& ( B != v_x ) )
| ( ( B = v_x )
& ( 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 @ v_y ) @ v_L )
& ( A != v_x ) )
| ( ( A = v_x )
& ( 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 @ v_y @ B ) @ v_L )
& ( B != v_x ) )
| ( ( B = v_x )
& ( A = v_y ) )
| ( ( 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 )
& ( B != v_x )
& ( A != v_x ) )
| ( ( A = v_x )
& ( 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 @ v_y ) @ v_L )
& ( B != v_x ) )
| ( ( B = v_x )
& ( 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 @ v_y @ A ) @ v_L )
& ( A != v_x ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(527,plain,
~ ( ! [A: $i,B: $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 @ B ) @ v_L )
& ( A != v_x )
& ( B != v_x ) )
=> ! [C: $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 @ B @ C ) @ v_L )
& ( C != v_x ) )
=> ( 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 @ C ) @ v_L ) )
& ( ( ( C = v_x )
& ( 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 @ v_y ) @ 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 @ v_y ) @ v_L ) ) ) )
& ( ( ( B = v_x )
& ( 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 @ v_y ) @ v_L )
& ( A != v_x ) )
=> ! [C: $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 @ v_y @ C ) @ v_L )
& ( C != v_x ) )
=> ( 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 @ C ) @ v_L ) ) )
& ( ( ( A = v_x )
& ( 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 @ v_y @ B ) @ v_L )
& ( B != v_x ) )
=> ! [C: $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 @ B @ C ) @ v_L )
& ( C != v_x ) )
=> ( ( C = v_y )
| ( 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 @ v_y @ C ) @ v_L ) ) )
& ( ( C = v_x )
=> ~ ( 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 @ v_y ) @ v_L ) ) ) ) )
& ! [A: $i,B: $i] :
( ( A != B )
=> ( ( ( A = v_x )
& ( B = v_y ) )
| ( ( 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 )
& ( A != v_x )
& ( B != v_x ) )
| ( ( B = v_x )
& ( 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 @ v_y ) @ v_L )
& ( A != v_x ) )
| ( ( A = v_x )
& ( 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 @ v_y @ B ) @ v_L )
& ( B != v_x ) )
| ( ( B = v_x )
& ( A = v_y ) )
| ( ( 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 )
& ( B != v_x )
& ( A != v_x ) )
| ( ( A = v_x )
& ( 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 @ v_y ) @ v_L )
& ( B != v_x ) )
| ( ( B = v_x )
& ( 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 @ v_y @ A ) @ v_L )
& ( A != v_x ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(103,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(877,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)],[103]) ).
thf(39,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(692,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)],[39]) ).
thf(238,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(1345,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)],[238]) ).
thf(141,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(988,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)],[141]) ).
thf(118,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(920,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)],[118]) ).
thf(444,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(2204,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)],[444]) ).
thf(504,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(2473,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)],[504]) ).
thf(321,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(1691,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)],[321]) ).
thf(121,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(925,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)],[121]) ).
thf(63,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(761,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)],[63]) ).
thf(422,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(2118,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)],[422]) ).
thf(235,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(1338,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)],[235]) ).
thf(269,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(1470,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)],[269]) ).
thf(356,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(1868,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)],[356]) ).
thf(450,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(2232,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)],[450]) ).
thf(467,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(2296,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)],[467]) ).
thf(413,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(2083,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)],[413]) ).
thf(159,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(1067,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)],[159]) ).
thf(333,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(1736,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)],[333]) ).
thf(512,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(2496,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)],[512]) ).
thf(78,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(798,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)],[78]) ).
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(1057,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(184,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(1163,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)],[184]) ).
thf(458,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(2264,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)],[458]) ).
thf(331,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(1723,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)],[331]) ).
thf(88,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(825,plain,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(301,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(1580,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)],[301]) ).
thf(211,axiom,
! [A: $i] : ( c_Relation_Otrans @ A @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Id) ).
thf(1255,plain,
! [A: $i] : ( c_Relation_Otrans @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
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(630,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(396,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(2015,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)],[396]) ).
thf(360,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(1883,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)],[360]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le1) ).
thf(1274,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(495,axiom,
v_x != v_y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2441,plain,
v_x != v_y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
= ( c_Relation_Oconverse @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converse) ).
thf(957,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
= ( c_Relation_Oconverse @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(108,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(894,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)],[108]) ).
thf(75,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(788,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)],[75]) ).
thf(430,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(2150,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)],[430]) ).
thf(373,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(1938,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)],[373]) ).
thf(382,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(1968,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)],[382]) ).
thf(264,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(1457,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)],[264]) ).
thf(182,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(1159,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)],[182]) ).
thf(160,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(1079,plain,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( 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 )
=> ( ( 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_Arrow__Order__Mirabelle_Obelow @ C @ E @ D ) )
<=> ( ( B != A )
& ( ( A = E )
=> ( 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 @ D ) @ C ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( 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 @ D @ A ) @ C ) ) )
& ( ( B != E )
=> ( 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 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__below) ).
thf(2345,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( 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 )
=> ( ( ( 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_Arrow__Order__Mirabelle_Obelow @ C @ E @ D ) )
=> ( ( B != A )
& ( ( A = E )
=> ( 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 @ D ) @ C ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( 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 @ D @ A ) @ C ) ) )
& ( ( B != E )
=> ( 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 ) ) ) ) ) )
& ( ( ( B != A )
& ( ( A = E )
=> ( 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 @ D ) @ C ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( 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 @ D @ A ) @ C ) ) )
& ( ( B != E )
=> ( 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 @ B @ A ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(197,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(1195,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)],[197]) ).
thf(252,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(1392,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)],[252]) ).
thf(366,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(1910,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)],[366]) ).
thf(361,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__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntI) ).
thf(1888,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__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
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(665,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(178,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(1143,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)],[178]) ).
thf(517,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(2515,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)],[517]) ).
thf(216,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(1270,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)],[216]) ).
thf(349,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(1804,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)],[349]) ).
thf(276,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(1498,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)],[276]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distrib__sup__le) ).
thf(1540,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(329,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(1719,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)],[329]) ).
thf(73,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(783,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Opreorder @ B )
=> ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(459,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(2268,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)],[459]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__inf__iff) ).
thf(1360,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(240,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(1350,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)],[240]) ).
thf(372,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(1936,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)],[372]) ).
thf(306,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 )
=> ( ( 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_Lin__irrefl) ).
thf(1592,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 )
=> ( ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(55,axiom,
class_Orderings_Oorder @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
thf(742,plain,
class_Orderings_Oorder @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(41,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(697,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)],[41]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ORange @ C @ B @ ( c_Relation_Oconverse @ B @ C @ A ) )
= ( c_Relation_ODomain @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__converse) ).
thf(1234,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ORange @ C @ B @ ( c_Relation_Oconverse @ B @ C @ A ) )
= ( c_Relation_ODomain @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Olinear__order__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
<=> ( c_Order__Relation_Olinear__order__on @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linear__order__on__converse) ).
thf(1089,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Order__Relation_Olinear__order__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
=> ( c_Order__Relation_Olinear__order__on @ C @ B @ A ) )
& ( ( c_Order__Relation_Olinear__order__on @ C @ B @ A )
=> ( c_Order__Relation_Olinear__order__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(513,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(2498,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)],[513]) ).
thf(25,axiom,
class_Orderings_Opreorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
thf(650,plain,
class_Orderings_Opreorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Orefl__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
<=> ( c_Relation_Orefl__on @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__converse) ).
thf(948,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Orefl__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
=> ( c_Relation_Orefl__on @ C @ B @ A ) )
& ( ( c_Relation_Orefl__on @ C @ B @ A )
=> ( c_Relation_Orefl__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(287,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(1534,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)],[287]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ D @ C ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) )
=> ~ ( ( c_member @ F @ D @ B )
=> ~ ( c_member @ E @ C @ ( hAPP @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaE2) ).
thf(1794,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ D @ C ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) )
=> ~ ( ( c_member @ F @ D @ B )
=> ~ ( c_member @ E @ C @ ( hAPP @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(377,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(1953,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)],[377]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
<=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__inf) ).
thf(1493,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A )
= B ) )
& ( ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A )
= B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(232,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(1329,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)],[232]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( 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_IntE) ).
thf(2323,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( 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)],[472]) ).
thf(123,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(933,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)],[123]) ).
thf(60,axiom,
class_Orderings_Olinorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(753,plain,
class_Orderings_Olinorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(191,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(1182,plain,
! [A: $i,B: $i] : ( c_Relation_Otrans @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
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(669,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(257,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(1424,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)],[257]) ).
thf(198,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(1214,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)],[198]) ).
thf(262,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(1446,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)],[262]) ).
thf(317,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(1644,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)],[317]) ).
thf(147,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(1016,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)],[147]) ).
thf(414,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(2085,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)],[414]) ).
thf(209,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(1249,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)],[209]) ).
thf(431,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(2153,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)],[431]) ).
thf(196,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(1192,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)],[196]) ).
thf(115,axiom,
! [A: $i] :
( ( c_Relation_Oconverse @ A @ A @ ( c_Relation_OId @ A ) )
= ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Id) ).
thf(911,plain,
! [A: $i] :
( ( c_Relation_Oconverse @ A @ A @ ( c_Relation_OId @ A ) )
= ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(50,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(721,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)],[50]) ).
thf(347,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(1799,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)],[347]) ).
thf(327,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(1715,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)],[327]) ).
thf(70,axiom,
class_Orderings_Opreorder @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
thf(779,plain,
class_Orderings_Opreorder @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(6,axiom,
class_Lattices_Osemilattice__sup @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
thf(605,plain,
class_Lattices_Osemilattice__sup @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(284,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(1525,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)],[284]) ).
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(647,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(144,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(997,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)],[144]) ).
thf(497,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(2450,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)],[497]) ).
thf(304,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(1588,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)],[304]) ).
thf(174,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(1131,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)],[174]) ).
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(654,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(406,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 ) @ ( c_Relation_Oconverse @ D @ E @ A ) )
=> ( c_member @ ( tc_prod @ D @ E ) @ ( c_Product__Type_OPair @ D @ E @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseD) ).
thf(2052,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 ) @ ( c_Relation_Oconverse @ D @ E @ A ) )
=> ( c_member @ ( tc_prod @ D @ E ) @ ( c_Product__Type_OPair @ D @ E @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetD) ).
thf(1599,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)],[308]) ).
thf(259,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(1434,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)],[259]) ).
thf(76,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(792,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)],[76]) ).
thf(525,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(2546,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)],[525]) ).
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(633,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(404,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(2043,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)],[404]) ).
thf(296,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(1563,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)],[296]) ).
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(2408,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(282,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(1515,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)],[282]) ).
thf(363,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(1895,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)],[363]) ).
thf(439,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(2189,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)],[439]) ).
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(953,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(163,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(1086,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)],[163]) ).
thf(125,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(938,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)],[125]) ).
thf(155,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(1054,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)],[155]) ).
thf(408,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(2057,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)],[408]) ).
thf(64,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(765,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oorder @ B )
=> ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(477,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(2338,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)],[477]) ).
thf(391,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(1996,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)],[391]) ).
thf(429,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(2144,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)],[429]) ).
thf(364,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(1906,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)],[364]) ).
thf(392,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(2001,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)],[392]) ).
thf(323,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(1698,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)],[323]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ C ) @ B @ ( c_Relation_Oconverse @ C @ D @ A ) )
=> ~ ! [E: $i,F: $i] :
( ( B
= ( c_Product__Type_OPair @ D @ C @ F @ E ) )
=> ~ ( c_member @ ( tc_prod @ C @ D ) @ ( c_Product__Type_OPair @ C @ D @ E @ F ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseE) ).
thf(2253,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ C ) @ B @ ( c_Relation_Oconverse @ C @ D @ A ) )
=> ~ ! [E: $i,F: $i] :
( ( B
= ( c_Product__Type_OPair @ D @ C @ F @ E ) )
=> ~ ( c_member @ ( tc_prod @ C @ D ) @ ( c_Product__Type_OPair @ C @ D @ E @ F ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(370,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(1927,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)],[370]) ).
thf(98,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(856,plain,
! [A: $i,B: $i] : ( c_Relation_Oantisym @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(247,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(1374,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)],[247]) ).
thf(52,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(733,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)],[52]) ).
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(601,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(134,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(965,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)],[134]) ).
thf(280,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(1510,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)],[280]) ).
thf(86,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(819,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)],[86]) ).
thf(112,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(904,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)],[112]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( 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 )
=> ( ( 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_Arrow__Order__Mirabelle_Oabove @ C @ E @ D ) )
<=> ( ( B != A )
& ( ( B = D )
=> ( 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 @ E @ A ) @ C ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( 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 @ E ) @ C ) ) )
& ( ( A != D )
=> ( 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 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__above) ).
thf(1833,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( 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 )
=> ( ( ( 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_Arrow__Order__Mirabelle_Oabove @ C @ E @ D ) )
=> ( ( B != A )
& ( ( B = D )
=> ( 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 @ E @ A ) @ C ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( 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 @ E ) @ C ) ) )
& ( ( A != D )
=> ( 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 ) ) ) ) ) )
& ( ( ( B != A )
& ( ( B = D )
=> ( 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 @ E @ A ) @ C ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( 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 @ E ) @ C ) ) )
& ( ( A != D )
=> ( 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 @ B @ A ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(368,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(1916,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)],[368]) ).
thf(447,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(2225,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)],[447]) ).
thf(93,axiom,
class_Groups_Ominus @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
thf(843,plain,
class_Groups_Ominus @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(519,axiom,
! [A: $i,B: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ B @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mktop__Lin) ).
thf(2525,plain,
! [A: $i,B: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ B @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
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__neqE) ).
thf(772,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)],[67]) ).
thf(483,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(2393,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)],[483]) ).
thf(371,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(1929,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)],[371]) ).
thf(56,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(743,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)],[56]) ).
thf(324,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(1701,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)],[324]) ).
thf(314,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(1615,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)],[314]) ).
thf(342,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(1784,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)],[342]) ).
thf(251,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(1389,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)],[251]) ).
thf(102,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(875,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)],[102]) ).
thf(47,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(711,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)],[47]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le2) ).
thf(1226,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(273,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(1488,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)],[273]) ).
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(641,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(176,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(1139,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)],[176]) ).
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(936,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(446,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(2220,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)],[446]) ).
thf(48,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(713,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)],[48]) ).
thf(205,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(1239,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)],[205]) ).
thf(233,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(1332,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)],[233]) ).
thf(44,axiom,
class_Orderings_Obot @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
thf(704,plain,
class_Orderings_Obot @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
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(672,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(320,axiom,
! [A: $i,B: $i,C: $i,D: $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 @ D @ C ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) )
<=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != 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 @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mkbot) ).
thf(1669,plain,
! [A: $i,B: $i,C: $i,D: $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 @ D @ C ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) )
=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != 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 @ D @ C ) @ B ) ) ) )
& ( ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != 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 @ D @ C ) @ 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 @ D @ C ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(441,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(2193,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)],[441]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ D @ C ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) )
<=> ( ( c_member @ F @ D @ B )
& ( c_member @ E @ C @ ( hAPP @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__Sigma__iff) ).
thf(1786,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ D @ C ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) )
=> ( ( c_member @ F @ D @ B )
& ( c_member @ E @ C @ ( hAPP @ A @ D ) ) ) )
& ( ( ( c_member @ F @ D @ B )
& ( c_member @ E @ C @ ( hAPP @ A @ D ) ) )
=> ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ D @ C ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
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(2029,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(473,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(2326,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)],[473]) ).
thf(325,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(1707,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)],[325]) ).
thf(466,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(2293,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)],[466]) ).
thf(499,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(2457,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)],[499]) ).
thf(80,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(804,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(138,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(979,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)],[138]) ).
thf(470,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(2311,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)],[470]) ).
thf(253,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(1408,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)],[253]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ D @ C ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) )
=> ( c_member @ E @ C @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaD2) ).
thf(2229,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ D @ C ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) )
=> ( c_member @ E @ C @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(491,axiom,
? [A: $i] : ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ A @ c_Arrow__Order__Mirabelle_OLin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linear__alt) ).
thf(2422,plain,
? [A: $i] : ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ A @ c_Arrow__Order__Mirabelle_OLin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(290,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(1542,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)],[290]) ).
thf(421,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(2116,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)],[421]) ).
thf(340,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(1771,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)],[340]) ).
thf(298,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(1571,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(188,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(1175,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)],[188]) ).
thf(488,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(2415,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)],[488]) ).
thf(511,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(2493,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)],[511]) ).
thf(299,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(1574,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)],[299]) ).
thf(350,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(1806,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)],[350]) ).
thf(145,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(1011,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)],[145]) ).
thf(455,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(2257,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)],[455]) ).
thf(142,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oantisym @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
<=> ( c_Relation_Oantisym @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__converse) ).
thf(990,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Oantisym @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
=> ( c_Relation_Oantisym @ B @ A ) )
& ( ( c_Relation_Oantisym @ B @ A )
=> ( c_Relation_Oantisym @ B @ ( c_Relation_Oconverse @ B @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(452,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(2246,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)],[452]) ).
thf(310,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(1603,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)],[310]) ).
thf(104,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(880,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)],[104]) ).
thf(153,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(1043,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)],[153]) ).
thf(83,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(811,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)],[83]) ).
thf(399,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(2025,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)],[399]) ).
thf(99,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(858,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)],[99]) ).
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(621,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(230,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(1325,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)],[230]) ).
thf(149,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(1029,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)],[149]) ).
thf(148,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(1022,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)],[148]) ).
thf(462,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(2278,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)],[462]) ).
thf(189,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(1177,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)],[189]) ).
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(609,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(420,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(2111,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)],[420]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Product__Type_OSigma @ C @ B @ ( 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_Sigma__empty1) ).
thf(2261,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Product__Type_OSigma @ C @ B @ ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
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(594,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(95,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(848,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)],[95]) ).
thf(42,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(700,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)],[42]) ).
thf(293,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(1556,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)],[293]) ).
thf(66,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(769,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)],[66]) ).
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(2289,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(187,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(1171,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)],[187]) ).
thf(411,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(2075,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)],[411]) ).
thf(271,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(1474,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)],[271]) ).
thf(89,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(827,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)],[89]) ).
thf(507,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(2481,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)],[507]) ).
thf(71,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(780,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( class_Orderings_Obot @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(140,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(986,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)],[140]) ).
thf(172,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(1113,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)],[172]) ).
thf(398,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(2022,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)],[398]) ).
thf(522,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(2535,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)],[522]) ).
thf(244,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(1364,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)],[244]) ).
thf(468,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(2303,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)],[468]) ).
thf(168,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(1102,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)],[168]) ).
thf(432,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(2156,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)],[432]) ).
thf(119,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(922,plain,
! [A: $i] : ( c_Relation_Osingle__valued @ A @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(384,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(1973,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)],[384]) ).
thf(29,axiom,
class_Lattices_Osemilattice__inf @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
thf(658,plain,
class_Lattices_Osemilattice__inf @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(515,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(2506,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)],[515]) ).
thf(484,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(2401,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)],[484]) ).
thf(307,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(1594,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)],[307]) ).
thf(427,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(2139,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)],[427]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oconverse @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Id__on) ).
thf(883,plain,
! [A: $i,B: $i] :
( ( c_Relation_Oconverse @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(394,axiom,
! [A: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A ) @ c_Arrow__Order__Mirabelle_OLin )
<=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ A @ c_Arrow__Order__Mirabelle_OLin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__in__Lin) ).
thf(2005,plain,
! [A: $i] :
( ( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A ) @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ A @ c_Arrow__Order__Mirabelle_OLin ) )
& ( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ A @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(407,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(2054,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)],[407]) ).
thf(302,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(1583,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)],[302]) ).
thf(319,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(1662,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)],[319]) ).
thf(338,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(1758,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)],[338]) ).
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(663,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(514,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oconverse @ 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 @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Un) ).
thf(2503,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oconverse @ 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 @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(423,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(2124,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)],[423]) ).
thf(175,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(1134,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)],[175]) ).
thf(236,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(1340,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)],[236]) ).
thf(270,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(1472,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)],[270]) ).
thf(379,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(1958,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)],[379]) ).
thf(61,axiom,
class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
thf(754,plain,
class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(77,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(795,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)],[77]) ).
thf(460,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(2271,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)],[460]) ).
thf(37,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(680,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)],[37]) ).
thf(161,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(1081,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)],[161]) ).
thf(58,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(749,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)],[58]) ).
thf(475,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(2333,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)],[475]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Oconverse @ C @ B @ ( c_Relation_Oconverse @ B @ C @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).
thf(1145,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Oconverse @ C @ B @ ( c_Relation_Oconverse @ B @ C @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
thf(836,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(291,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(1551,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)],[291]) ).
thf(516,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(2513,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)],[516]) ).
thf(101,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(872,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)],[101]) ).
thf(46,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(707,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)],[46]) ).
thf(107,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(887,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)],[107]) ).
thf(311,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(1605,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)],[311]) ).
thf(210,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(1252,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)],[210]) ).
thf(53,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(739,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ominus @ B )
=> ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(215,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(1267,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)],[215]) ).
thf(434,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 @ ( tc_prod @ D @ E ) @ ( c_Product__Type_OPair @ D @ E @ B @ C ) @ ( c_Relation_Oconverse @ E @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseI) ).
thf(2160,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 @ ( tc_prod @ D @ E ) @ ( c_Product__Type_OPair @ D @ E @ B @ C ) @ ( c_Relation_Oconverse @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(45,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(705,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)],[45]) ).
thf(312,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(1611,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)],[312]) ).
thf(387,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(1987,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)],[387]) ).
thf(353,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(1813,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)],[353]) ).
thf(193,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(1186,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)],[193]) ).
thf(151,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(1038,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)],[151]) ).
thf(49,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(717,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)],[49]) ).
thf(92,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(840,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)],[92]) ).
thf(425,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(2128,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)],[425]) ).
thf(227,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(1317,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)],[227]) ).
thf(509,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(2486,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)],[509]) ).
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(643,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(502,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(2468,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)],[502]) ).
thf(113,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(907,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)],[113]) ).
thf(334,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(1738,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)],[334]) ).
thf(199,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(1218,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)],[199]) ).
thf(212,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(1257,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)],[212]) ).
thf(43,axiom,
class_Lattices_Olattice @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
thf(703,plain,
class_Lattices_Olattice @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(524,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(2543,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)],[524]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Opreorder__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
<=> ( c_Order__Relation_Opreorder__on @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_preorder__on__converse) ).
thf(1221,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Order__Relation_Opreorder__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
=> ( c_Order__Relation_Opreorder__on @ C @ B @ A ) )
& ( ( c_Order__Relation_Opreorder__on @ C @ B @ A )
=> ( c_Order__Relation_Opreorder__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ODomain @ C @ B @ ( c_Relation_Oconverse @ B @ C @ A ) )
= ( c_Relation_ORange @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__converse) ).
thf(1504,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ODomain @ C @ B @ ( c_Relation_Oconverse @ B @ C @ A ) )
= ( c_Relation_ORange @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(346,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(1797,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)],[346]) ).
thf(328,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(1717,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)],[328]) ).
thf(246,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(1372,plain,
! [A: $i,B: $i] : ( c_Wellfounded_Owf @ B @ ( hAPP @ ( c_Wellfounded_Omeasure @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i,D: $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 @ D @ C ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) )
<=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != 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 @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mktop) ).
thf(1617,plain,
! [A: $i,B: $i,C: $i,D: $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 @ D @ C ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) )
=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != 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 @ D @ C ) @ B ) ) ) )
& ( ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != 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 @ D @ C ) @ 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 @ D @ C ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(177,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(1141,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)],[177]) ).
thf(493,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(2426,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)],[493]) ).
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(656,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(348,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_Oconverse @ D @ D @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ ( c_Relation_Oconverse @ D @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converseI) ).
thf(1802,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_Oconverse @ D @ D @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ ( c_Relation_Oconverse @ D @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(336,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(1749,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)],[336]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( 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 ) @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Int__assoc__eq) ).
thf(1427,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( 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 ) @ A @ C ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( 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)],[258]) ).
thf(303,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(1585,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)],[303]) ).
thf(165,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(1094,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)],[165]) ).
thf(359,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(1881,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)],[359]) ).
thf(217,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(1272,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)],[217]) ).
thf(10,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(612,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)],[10]) ).
thf(374,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(1940,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)],[374]) ).
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(627,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(162,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(1084,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)],[162]) ).
thf(506,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(2479,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)],[506]) ).
thf(94,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(844,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)],[94]) ).
thf(170,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(1108,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)],[170]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ORange @ C @ B @ A )
= ( c_Relation_ODomain @ B @ C @ ( c_Relation_Oconverse @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__def) ).
thf(1459,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ORange @ C @ B @ A )
= ( c_Relation_ODomain @ B @ C @ ( c_Relation_Oconverse @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(405,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(2045,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)],[405]) ).
thf(412,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(2078,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)],[412]) ).
thf(367,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(1913,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)],[367]) ).
thf(438,axiom,
! [A: $i,B: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ B @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
thf(2187,plain,
! [A: $i,B: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ B @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(194,axiom,
c_Relation_Otrans @ tc_Nat_Onat @ c_Wellfounded_Oless__than,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__than) ).
thf(1189,plain,
c_Relation_Otrans @ tc_Nat_Onat @ c_Wellfounded_Oless__than,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(330,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(1721,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)],[330]) ).
thf(416,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(2098,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)],[416]) ).
thf(316,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(1639,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)],[316]) ).
thf(453,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(2251,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)],[453]) ).
thf(485,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(2406,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)],[485]) ).
thf(521,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(2532,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)],[521]) ).
thf(17,axiom,
class_Groups_Ominus @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
thf(632,plain,
class_Groups_Ominus @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(494,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(2431,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)],[494]) ).
thf(207,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(1244,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)],[207]) ).
thf(219,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(1276,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)],[219]) ).
thf(305,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(1590,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)],[305]) ).
thf(133,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(963,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
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(2273,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(437,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(2174,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)],[437]) ).
thf(464,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(2283,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)],[464]) ).
thf(143,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(995,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)],[143]) ).
thf(294,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(1558,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)],[294]) ).
thf(274,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(1491,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)],[274]) ).
thf(116,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(914,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)],[116]) ).
thf(261,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(1440,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)],[261]) ).
thf(435,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(2162,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)],[435]) ).
thf(281,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(1513,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)],[281]) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( c_Relation_OField @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
= ( c_Relation_OField @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__converse) ).
thf(899,plain,
! [A: $i,B: $i] :
( ( c_Relation_OField @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
= ( c_Relation_OField @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(403,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(2036,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)],[403]) ).
thf(390,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(1994,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)],[390]) ).
thf(154,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(1045,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)],[154]) ).
thf(183,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(1161,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)],[183]) ).
thf(239,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(1348,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)],[239]) ).
thf(12,axiom,
class_Orderings_Oord @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(620,plain,
class_Orderings_Oord @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(518,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(2517,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)],[518]) ).
thf(481,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(2385,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)],[481]) ).
thf(166,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(1097,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)],[166]) ).
thf(358,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(1876,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)],[358]) ).
thf(97,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(854,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)],[97]) ).
thf(365,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(1908,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)],[365]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ D @ C ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) )
=> ( c_member @ F @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaD1) ).
thf(2003,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ D @ C ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) )
=> ( c_member @ F @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(428,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(2142,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)],[428]) ).
thf(332,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(1725,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)],[332]) ).
thf(220,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(1280,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)],[220]) ).
thf(285,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Otrans @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
<=> ( c_Relation_Otrans @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__converse) ).
thf(1527,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Otrans @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
=> ( c_Relation_Otrans @ B @ A ) )
& ( ( c_Relation_Otrans @ B @ A )
=> ( c_Relation_Otrans @ B @ ( c_Relation_Oconverse @ B @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(180,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(1148,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( c_fequal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(81,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(807,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)],[81]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ A @ tc_HOL_Obool ) @ D @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1I) ).
thf(1561,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ A @ tc_HOL_Obool ) @ D @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(326,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(1710,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)],[326]) ).
thf(415,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(2091,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)],[415]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
thf(1065,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(40,axiom,
class_Lattices_Osemilattice__inf @ tc_HOL_Obool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
thf(696,plain,
class_Lattices_Osemilattice__inf @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
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(955,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(443,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(2201,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)],[443]) ).
thf(79,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(801,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)],[79]) ).
thf(388,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(1989,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)],[388]) ).
thf(234,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(1335,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)],[234]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ D ) @ C @ ( c_Product__Type_OSigma @ E @ D @ B @ A ) )
=> ~ ! [F: $i] :
( ( c_member @ E @ F @ B )
=> ! [G: $i] :
( ( c_member @ D @ G @ ( hAPP @ A @ F ) )
=> ( C
!= ( c_Product__Type_OPair @ E @ D @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaE) ).
thf(1693,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ D ) @ C @ ( c_Product__Type_OSigma @ E @ D @ B @ A ) )
=> ~ ! [F: $i] :
( ( c_member @ E @ F @ B )
=> ! [G: $i] :
( ( c_member @ D @ G @ ( hAPP @ A @ F ) )
=> ( C
!= ( c_Product__Type_OPair @ E @ D @ F @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(109,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(897,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)],[109]) ).
thf(65,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(767,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)],[65]) ).
thf(489,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(2417,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)],[489]) ).
thf(132,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(960,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)],[132]) ).
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(635,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(478,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(2340,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)],[478]) ).
thf(185,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(1165,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)],[185]) ).
thf(106,axiom,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Opred__nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pred__nat) ).
thf(886,plain,
c_Wellfounded_Owf @ tc_Nat_Onat @ c_Wellfounded_Opred__nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Ototal__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
<=> ( c_Relation_Ototal__on @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__converse) ).
thf(928,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Ototal__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
=> ( c_Relation_Ototal__on @ C @ B @ A ) )
& ( ( c_Relation_Ototal__on @ C @ B @ A )
=> ( c_Relation_Ototal__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
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(624,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(241,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
<=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__converse) ).
thf(1352,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Oacyclic @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
=> ( c_Wellfounded_Oacyclic @ B @ A ) )
& ( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ ( c_Relation_Oconverse @ B @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(173,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(1129,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)],[173]) ).
thf(181,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(1152,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)],[181]) ).
thf(286,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(1532,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)],[286]) ).
thf(288,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(1537,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)],[288]) ).
thf(385,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(1976,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)],[385]) ).
thf(242,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(1357,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)],[242]) ).
thf(369,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(1923,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)],[369]) ).
thf(87,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(822,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)],[87]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ~ ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1E) ).
thf(850,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ~ ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(139,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(982,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)],[139]) ).
thf(222,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(1299,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)],[222]) ).
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(607,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(228,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(1320,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)],[228]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distrib__inf__le) ).
thf(1184,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(30,axiom,
class_Orderings_Oorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
thf(659,plain,
class_Orderings_Oorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(68,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(775,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)],[68]) ).
thf(440,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(2191,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)],[440]) ).
thf(418,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(2106,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)],[418]) ).
thf(471,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(2321,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)],[471]) ).
thf(245,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(1367,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)],[245]) ).
thf(339,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(1769,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)],[339]) ).
thf(62,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(755,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)],[62]) ).
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(676,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(268,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(1468,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)],[268]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ C @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) )
=> ~ ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ A @ A ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__tranclI) ).
thf(2470,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ C @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) )
=> ~ ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ A @ A ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(255,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(1417,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)],[255]) ).
thf(357,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(1870,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)],[357]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Opartial__order__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
<=> ( c_Order__Relation_Opartial__order__on @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partial__order__on__converse) ).
thf(972,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Order__Relation_Opartial__order__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
=> ( c_Order__Relation_Opartial__order__on @ C @ B @ A ) )
& ( ( c_Order__Relation_Opartial__order__on @ C @ B @ A )
=> ( c_Order__Relation_Opartial__order__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(2601,plain,
$false,
inference(cvc4,[status(thm)],[645,2199,1036,1411,1190,2306,2072,1105,909,2463,1315,941,777,1818,1501,2452,809,2336,2109,2131,2031,2412,1237,1179,2331,1956,1950,1554,1110,977,2104,683,1808,2527,741,2380,1971,597,1437,1422,1569,1041,861,1655,2459,945,1507,1756,1310,814,1327,2476,1260,1342,747,2227,782,2020,1613,2010,2067,1518,1228,651,2491,2548,1782,1601,1386,724,1792,1985,785,1313,1577,1992,2126,2444,1264,2217,1323,619,838,917,751,1462,1059,2420,638,1379,2169,1247,1890,1479,1013,1741,2158,1963,2388,1100,817,902,969,606,2237,924,1302,2259,1960,1283,1946,1465,1811,1450,2540,2034,1169,1377,2281,2483,2424,660,1242,527,877,692,1345,988,920,2204,2473,1691,925,761,2118,1338,1470,1868,2232,2296,2083,1067,1736,2496,798,1057,1163,2264,1723,825,1580,1255,630,2015,1883,1274,2441,957,894,788,2150,1938,1968,1457,1159,1079,2345,1195,1392,1910,1888,665,1143,2515,1270,1804,1498,1540,1719,783,2268,1360,1350,1936,1592,742,697,1234,1089,2498,650,948,1534,1794,1953,1493,1329,2323,933,753,1182,669,1424,1214,1446,1644,1016,2085,1249,2153,1192,911,721,1799,1715,779,605,1525,647,997,2450,1588,1131,654,2052,1599,1434,792,2546,633,2043,1563,2408,1515,1895,2189,953,1086,938,1054,2057,765,2338,1996,2144,1906,2001,1698,2253,1927,856,1374,733,601,965,1510,819,904,1833,1916,2225,843,2525,772,2393,1929,743,1701,1615,1784,1389,875,711,1226,1488,641,1139,936,2220,713,1239,1332,704,672,1669,2193,1786,2029,2326,1707,2293,2457,804,979,2311,1408,2229,2422,1542,2116,1771,1571,1175,2415,2493,1574,1806,1011,2257,990,2246,1603,880,1043,811,2025,858,621,1325,1029,1022,2278,1177,609,2111,2261,594,848,700,1556,769,2289,1171,2075,1474,827,2481,780,986,1113,2022,2535,1364,2303,1102,2156,922,1973,658,2506,2401,1594,2139,883,2005,2054,1583,1662,1758,663,2503,2124,1134,1340,1472,1958,754,795,2271,680,1081,749,2333,1145,836,1551,2513,872,707,887,1605,1252,739,1267,2160,705,1611,1987,1813,1186,1038,717,840,2128,1317,2486,643,2468,907,1738,1218,1257,703,2543,1221,1504,1797,1717,1372,1617,1141,2426,656,1802,1749,1427,1585,1094,1881,1272,612,1940,627,1084,2479,844,1108,1459,2045,2078,1913,2187,1189,1721,2098,1639,2251,2406,2532,632,2431,1244,1276,1590,963,2273,2174,2283,995,1558,1491,914,1440,2162,1513,899,2036,1994,1045,1161,1348,620,2517,2385,1097,1876,854,1908,2003,2142,1725,1280,1527,1148,807,1561,1710,2091,1065,696,955,2201,801,1989,1335,1693,897,767,2417,960,635,2340,1165,886,928,624,1352,1129,1152,1532,1537,1976,1357,1923,822,850,982,1299,607,1320,1184,659,775,2191,2106,2321,1367,1769,755,676,1468,2470,1417,1870,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SCT115+1 : TPTP v8.1.2. Released v5.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n025.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 15:41:34 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.85/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.48/1.07 % [INFO] Parsing done (216ms).
% 1.82/1.07 % [INFO] Running in sequential loop mode.
% 2.28/1.26 % [INFO] eprover registered as external prover.
% 2.28/1.26 % [INFO] cvc4 registered as external prover.
% 2.28/1.27 % [INFO] Scanning for conjecture ...
% 2.80/1.40 % [INFO] Found a conjecture and 527 axioms. Running axiom selection ...
% 3.29/1.53 % [INFO] Axiom selection finished. Selected 524 axioms (removed 3 axioms).
% 3.86/1.75 % [INFO] Problem is first-order (TPTP FOF).
% 3.86/1.77 % [INFO] Type checking passed.
% 4.15/1.77 % [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 ...
% 19.04/5.08 % External prover 'cvc4' found a proof!
% 19.04/5.08 % [INFO] Killing All external provers ...
% 19.04/5.08 % Time passed: 4549ms (effective reasoning time: 3999ms)
% 19.04/5.08 % 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)>
% 19.04/5.08 % Axioms used in derivation (524): fact_wf__not__refl, fact_order__le__neq__trans, fact_converseI, 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_converse__converse, fact_acc__wfI, fact_Field__empty, fact_Un__absorb1, fact_xt1_I1_J, fact_converse__rtrancl__induct2, fact_singleton__iff, fact_Diff__insert__absorb, arity_fun__Orderings_Oorder, fact_cut__apply, fact_le__inf__iff, fact_sup1I1, fact_order__le__less__trans, fact_insert__iff, arity_Nat__Onat__Lattices_Olattice, 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_prod_Orecs, fact_linorder__not__le, fact_curry__conv, fact_IdI, fact_insertI1, fact_order__less__asym_H, fact_Un__empty__left, fact_less__supI1, fact_bot__apply, fact_trancl__id, fact_mono__Field, fact_in__mktop, fact_linorder__antisym__conv2, arity_HOL__Obool__Orderings_Opreorder, fact_in__mkbot, fact_linorder__neqE, fact_sup__assoc, fact_curryE, fact_leI, fact_empty__not__insert, fact_rtrancl__empty, fact_order__eq__refl, fact_Un__insert__left, arity_fun__Lattices_Olattice, fact_rtrancl_Ortrancl__refl, fact_acc_Osimps, arity_Nat__Onat__Lattices_Osemilattice__inf, fact_SigmaE2, fact_trans__Id__on, fact_r__into__trancl_H, fact_converse__rtrancl__induct, fact_inf__sup__ord_I2_J, help_c__fequal__2, fact_acyclic__impl__antisym__rtrancl, fact_tranclD2, fact_linorder__antisym__conv3, fact_order__less__imp__not__eq, fact_rtrancl__mono, fact_rtrancl__subset__rtrancl, fact_insert__not__empty, fact_converse__rtranclE2, fact_split__paired__All, fact_Diff__subset, fact_acyclic__converse, fact_sup__absorb1, fact_equalityD2, fact_antisymI, fact_rtrancl__converse, fact_Sigma__empty1, fact_Field__Un, fact_less__eq, fact_Range__empty, fact_rev__ImageI, fact_linorder__antisym__conv1, fact_tranclE, fact_linear__alt, fact_acc_OaccI, fact_le__supI, fact_le__supI2, fact_single__valued__Id, fact_sup__ge2, fact_Diff__idemp, fact_singleton__inject, fact_le__funD, fact_emptyE, fact_le__fun__def, fact_acc__subset, fact_DiffD2, fact_wf__measure, fact_wf__irrefl, fact_linorder__less__linear, fact_Image__Un, fact_order__less__imp__not__less, fact_lnear__order__on__empty, fact_Domain__empty__iff, fact_ord__less__eq__trans, fact_in__mono, fact_Domain__Un__eq, fact_wf__lex__prod, fact_xt1_I9_J, fact_Diff__subset__conv, fact_DiffE, arity_fun__Lattices_Osemilattice__inf, fact_sup__least, fact_mkbot__Lin, arity_HOL__Obool__Lattices_Olattice, fact_in__measure, fact_minus__apply, fact_rtrancl__subset, fact_subset__singletonD, fact_Field__converse, fact_sup__eq__bot__iff, fact_single__valued__subset, fact_insert__is__Un, fact_wfE__pf, fact_subset__iff__psubset__eq, fact_Id__on__iff, fact_Diff__insert, fact_tfl__cut__apply, fact_converseE, 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_trancl__converse, fact_converse__inv__image, fact_xt1_I10_J, fact_order__antisym, fact_refl__onD, fact_sup__bot__left, fact_order__refl, arity_fun__Lattices_Osemilattice__sup, fact_acc__downwards, fact_distrib__inf__le, fact_Un__left__commute, fact_sup1I2, fact_inf1I, 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_rtrancl__reflcl__absorb, 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_predicate1D, fact_DomainI, fact_inf__sup__ord_I1_J, fact_inf1E, 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_eq__mem, fact_trans__diff__Id, 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_partial__order__on__converse, fact_equals0D, fact_insert__absorb, fact_rtrancl__converseI, fact_subset__insert, fact_Un__Image, fact_pair__in__Id__conv, 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_trancl__converseD, fact_in__below, fact_wf__converse__trancl, help_c__fequal__1, fact_in__above, fact_refl__on__Un, fact_linorder__neq__iff, fact_DiffD1, arity_Nat__Onat__Orderings_Oord, fact_irrefl__def, fact_UnI2, fact_distrib__sup__le, 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_Image__Int__subset, fact_set__mp, fact_less__than__iff, fact_Image__singleton__iff, fact_not__less__iff__gr__or__eq, fact_mktop__Lin, 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_le__iff__inf, fact_SigmaE, 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_Un__Int__assoc__eq, fact_partial__order__on__empty, fact_Pair__inject, fact_xt1_I12_J, fact_linear__order__on__def, fact_subset__refl, fact_inf__le1, fact_le__supE, fact_acc__wfD, 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, 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_linorder__le__cases, fact_converse__iff, fact_Id__on__eqI, fact_trancl__range, fact_acyclic__def, fact_order__less__le__trans, fact_rtrancl__eq__or__trancl, fact_trans__converse, fact_refl__onD1, fact_not__leE, fact_leD, fact_total__on__empty, fact_insert__ident, fact_subset__Image__Image__iff, fact_curryD, fact_subset__empty, fact_singletonE, fact_trancl_Or__into__trancl, 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, fact_acyclic__subset, fact_linear__order__on__converse, 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_tranclD, fact_Domain__iff, fact_DiffI, fact_eq__mem__trans, fact_antisymD, fact_mem__Sigma__iff, fact_acc__downwards__aux, fact_Un__empty__right, fact_trancl__converseI, fact_converse__Id__on, fact_set__rev__mp, fact_converse__in__Lin, fact_trans__lex__prod, fact_SigmaI, fact_wf__insert, fact_converseD, fact_Range__def, fact_rtrancl__induct, fact_sup__commute, fact_antisym__converse, fact_linorder__linear, fact_total__on__diff__Id, fact_transD, fact_trancl__into__trancl2, fact_single__valuedI, fact_subset__insertI2, fact_Un__absorb2, fact_single__valued__def, fact_trancl__rtrancl__absorb, arity_HOL__Obool__Lattices_Osemilattice__inf, fact_DomainE, fact_xt1_I6_J, fact_strict__linear__order__on__diff__Id, fact_in__lex__prod, fact_strict__linear__order__on__def, fact_wf__trancl, fact_ball__Un, fact_Un__upper1, fact_xt1_I2_J, conj_1, fact_antisym__reflcl, fact_UnCI, fact_linorder__not__less, fact_less__fun__def, fact_rev__predicate1D, fact_insert__Diff, fact_trans__rtrancl, fact_inf__sup__aci_I5_J, fact_SigmaD2, fact_Domain__Id__on, fact_cuts__eq, fact_equalityE, fact_Pair__eq, fact_tfl__wfrec, fact_in__rel__def, fact_inf__sup__ord_I4_J, fact_le__sup__iff, fact_refl__on__converse, 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_Lin__irrefl, fact_empty__subsetI, fact_insert__Diff__if, fact_insert__mono, fact_ord__eq__less__trans, fact_sup_Ocommute, fact_Un__Diff__cancel2, fact_Domain__converse, fact_Range__Un__eq, fact_less__supI2, fact_inf__le2, fact_wf__mlex, arity_fun__Groups_Ominus, fact_Nitpick_Owf__wfrec_H__def, 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_total__on__converse, fact_trancl__rtrancl__trancl, fact_sup1E, fact_inf__sup__aci_I7_J, fact_inf__sup__ord_I3_J, fact_IntI, fact_irrefl__tranclI, fact_wf__same__fst, fact_diff__eq__diff__less__eq, fact_Id__on__empty, fact_inf__sup__aci_I6_J, 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_diff__eq__diff__eq, fact_order__le__imp__less__or__eq, fact_antisym__Id__on, fact_order__antisym__conv, fact_Un__commute, fact_eqelem__imp__iff, arity_HOL__Obool__Orderings_Obot, fact_Image__iff, fact_Diff__iff, fact_preorder__on__converse, fact_sup__bot__right, fact_converse__Un, fact_psubset__subset__trans, fact_Un__least, fact_curryI, fact_well__order__on__def, fact_wf__acyclic, fact_subset__trans, fact_IntE, fact_sup__absorb2, fact_order__less__imp__le, fact_order__less__trans, fact_Range__converse, fact_trans__trancl, fact_Un__upper2, fact_SigmaD1, fact_antisym__Id, fact_order__less__irrefl, fact_Un__left__absorb, fact_order__le__less, fact_sup_Oleft__idem, fact_wf__asym, fact_not__psubset__empty, fact_Partial__order__eq__Image1__Image1__iff, conj_0, fact_mem__def, fact_refl__on__Id__on, fact_trancl__mono, fact_ord__eq__le__trans, fact_UnE, fact_fold__graph_H_Oequations_I2_J, fact_Field__insert, fact_rtrancl__converseD, fact_wfrec__rel_Osimps, fact_sup_Oleft__commute, fact_linorder__cases, fact_xt1_I11_J, 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_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, fact_trancl__reflcl, fact_converse__Id
% 19.04/5.08 % No. of inferences in proof: 1052
% 19.04/5.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4549 ms resp. 3999 ms w/o parsing
% 19.70/5.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.70/5.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------