TSTP Solution File: SCT128+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT128+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 11:50:40 EDT 2023
% Result : Theorem 178.58s 40.76s
% Output : Refutation 179.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 608
% Syntax : Number of formulae : 1234 ( 325 unt; 91 typ; 0 def)
% Number of atoms : 2931 ( 831 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 30655 ( 415 ~; 156 |; 223 &;28474 @)
% ( 92 <=>;1295 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 195 ( 195 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 91 usr; 20 con; 0-6 aty)
% Number of variables : 4244 ( 0 ^;4203 !; 41 ?;4244 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_member_type,type,
c_member: $i > $i ).
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 ).
thf(v_a_____type,type,
v_a____: $i ).
thf(v_b_____type,type,
v_b____: $i ).
thf(v_F_type,type,
v_F: $i ).
thf(v_Q_____type,type,
v_Q____: $i ).
thf(class_Lattices_Obounded__lattice_type,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(c_Lattices_Osemilattice__sup__class_Osup_type,type,
c_Lattices_Osemilattice__sup__class_Osup: $i > $i ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(c_Lattices_Osemilattice__inf__class_Oinf_type,type,
c_Lattices_Osemilattice__inf__class_Oinf: $i > $i ).
thf(class_Lattices_Osemilattice__sup_type,type,
class_Lattices_Osemilattice__sup: $i > $o ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $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(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Relation_OId__on_type,type,
c_Relation_OId__on: $i > $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Fun_Ofun__upd_type,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(c_Set_Othe__elem_type,type,
c_Set_Othe__elem: $i > $i > $i ).
thf(c_FuncSet_Oextensional__funcset_type,type,
c_FuncSet_Oextensional__funcset: $i > $i > $i > $i > $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_HOL_Oundefined_type,type,
c_HOL_Oundefined: $i > $i ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Transitive__Closure_Ortranclp_type,type,
c_Transitive__Closure_Ortranclp: $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_Product__Type_OSigma_type,type,
c_Product__Type_OSigma: $i > $i > $i > $i > $i ).
thf(class_Lattices_Osemilattice__inf_type,type,
class_Lattices_Osemilattice__inf: $i > $o ).
thf(class_Lattices_Odistrib__lattice_type,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(c_Relation_OField_type,type,
c_Relation_OField: $i > $i > $i ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(c_Relation_Ototal__on_type,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(c_FuncSet_OPi_type,type,
c_FuncSet_OPi: $i > $i > $i > $i > $i ).
thf(c_Relation_Osingle__valued_type,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(c_FuncSet_Oextensional_type,type,
c_FuncSet_Oextensional: $i > $i > $i > $i ).
thf(class_Lattices_Obounded__lattice__bot_type,type,
class_Lattices_Obounded__lattice__bot: $i > $o ).
thf(c_Wellfounded_Oaccp_type,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(v_a_H_____type,type,
v_a_H____: $i ).
thf(v_b_H_____type,type,
v_b_H____: $i ).
thf(c_Relation_Orefl__on_type,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(c_fequal_type,type,
c_fequal: $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i ).
thf(c_Wellfounded_Oacc_type,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(c_Wellfounded_Olex__prod_type,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OLin_type,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(c_Arrow__Order__Mirabelle_Obelow_type,type,
c_Arrow__Order__Mirabelle_Obelow: $i > $i > $i > $i ).
thf(c_Product__Type_Ocurry_type,type,
c_Product__Type_Ocurry: $i > $i > $i > $i > $i > $i > $i ).
thf(v_P_____type,type,
v_P____: $i ).
thf(v_P_H_____type,type,
v_P_H____: $i ).
thf(c_Recdef_Ocut_type,type,
c_Recdef_Ocut: $i > $i > $i ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oindi_type,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(c_Arrow__Order__Mirabelle_OProf_type,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
thf(c_Recdef_Owfrec__rel_type,type,
c_Recdef_Owfrec__rel: $i > $i > $i > $i > $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_COMBI_type,type,
c_COMBI: $i > $i ).
thf(c_HOL_OLet_type,type,
c_HOL_OLet: $i > $i > $i > $i > $i ).
thf(c_If_type,type,
c_If: $i > $i > $i ).
thf(c_COMBS_type,type,
c_COMBS: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Oabove_type,type,
c_Arrow__Order__Mirabelle_Oabove: $i ).
thf(c_Wellfounded_Oacyclic_type,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(c_FuncSet_Ocompose_type,type,
c_FuncSet_Ocompose: $i > $i > $i > $i > $i > $i > $i ).
thf(c_FuncSet_Orestrict_type,type,
c_FuncSet_Orestrict: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omktop_type,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(c_Relation_Oirrefl_type,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(c_Arrow__Order__Mirabelle_Ounanimity_type,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
thf(c_Arrow__Order__Mirabelle_Omkbot_type,type,
c_Arrow__Order__Mirabelle_Omkbot: $i > $i > $i ).
thf(c_fNot_type,type,
c_fNot: $i ).
thf(c_Predicate_ORangeP_type,type,
c_Predicate_ORangeP: $i > $i > $i > $i > $o ).
thf(c_Arrow__Order__Mirabelle_Odictator_type,type,
c_Arrow__Order__Mirabelle_Odictator: $i > $i > $o ).
thf(c_Arrow__Order__Mirabelle_OIIA_type,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
thf(c_Predicate_ODomainP_type,type,
c_Predicate_ODomainP: $i > $i > $i > $i > $o ).
thf(c_Recdef_Oadm__wf_type,type,
c_Recdef_Oadm__wf: $i > $i > $i > $i > $o ).
thf(c_Product__Type_Oprod_Oprod__rec_type,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Product__Type_Ointernal__split_type,type,
c_Product__Type_Ointernal__split: $i > $i > $i > $i > $i > $i ).
thf(c_Wellfounded_Omlex__prod_type,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(c_Relation_Oinv__image_type,type,
c_Relation_Oinv__image: $i > $i > $i > $i > $i ).
thf(c_Wellfounded_Oless__than_type,type,
c_Wellfounded_Oless__than: $i ).
thf(c_Nitpick_Orefl_H_type,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(c_FunDef_Oin__rel_type,type,
c_FunDef_Oin__rel: $i > $i > $i > $i > $i > $o ).
thf(c_Recdef_Osame__fst_type,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(456,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) )
=> ~ ! [H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).
thf(2199,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ C ) @ B ) )
=> ~ ! [H: $i,I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ E ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ F ) @ H ) @ I ) ) @ ( hAPP @ ( hAPP @ ( 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)],[456]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A )
= C )
<=> ( ( hAPP @ C @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
thf(1036,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A )
= C )
=> ( ( hAPP @ C @ B )
= A ) )
& ( ( ( hAPP @ C @ B )
= A )
=> ( ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
thf(1879,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__trans) ).
thf(1411,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(360,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ D @ C ) @ B ) @ A ) )
<=> ( ( A = B )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ D @ C ) @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclp_Oequations_I2_J) ).
thf(1823,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ D @ C ) @ B ) @ A ) )
=> ( ( A = B )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ D @ C ) @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) ) ) )
& ( ( ( A = B )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ D @ C ) @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ D @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(492,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_le__sup__iff) ).
thf(2341,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_FunDef_Oin__rel @ E @ D @ C @ B @ A )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
thf(2336,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_FunDef_Oin__rel @ E @ D @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) @ C ) )
=> ( c_FunDef_Oin__rel @ E @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le2) ).
thf(2072,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
thf(1237,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) )
=> ( 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 @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_Un__empty__left) ).
thf(523,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( 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)],[5]) ).
thf(524,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( 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(cnf,[status(esa)],[523]) ).
thf(525,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( 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(lifteq,[status(thm)],[524]) ).
thf(1,conjecture,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_Q____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_Q____ ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(519,plain,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_Q____ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(2452,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ A ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
!= ( hAPP @ v_F @ v_Q____ ) ) ),
inference(paramod_ordered,[status(thm)],[525,519]) ).
thf(2457,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ A ) )
| ( ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
!= v_F )
| ( A != v_Q____ ) ),
inference(simp,[status(thm)],[2452]) ).
thf(2463,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ v_Q____ ) )
| ( ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
!= v_F ) ),
inference(simp,[status(thm)],[2457]) ).
thf(363,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/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
thf(1840,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)],[363]) ).
thf(512,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel2) ).
thf(2427,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(55,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 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__mono) ).
thf(666,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 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
thf(1110,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I4_J) ).
thf(1686,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(46,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) @ ( c_Product__Type_OSigma @ B @ B @ ( c_Relation_OField @ B @ A ) @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ B @ ( c_Relation_OField @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Field2) ).
thf(645,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) @ ( c_Product__Type_OSigma @ B @ B @ ( c_Relation_OField @ B @ A ) @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ B @ ( c_Relation_OField @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__assoc) ).
thf(892,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Osemilattice__inf @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
thf(777,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)],[89]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Ofun__upd @ F @ E @ ( c_Fun_Ofun__upd @ F @ E @ D @ C @ B ) @ C @ A )
= ( c_Fun_Ofun__upd @ F @ E @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__upd) ).
thf(555,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Fun_Ofun__upd @ F @ E @ ( c_Fun_Ofun__upd @ F @ E @ D @ C @ B ) @ C @ A )
= ( c_Fun_Ofun__upd @ F @ E @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(497,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__distrib1) ).
thf(2363,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge1) ).
thf(1750,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__commute) ).
thf(1211,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(459,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD1) ).
thf(2210,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',fact_total__on__empty) ).
thf(682,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)],[61]) ).
thf(683,plain,
! [B: $i,A: $i] : ( c_Relation_Ototal__on @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ),
inference(cnf,[status(esa)],[682]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(730,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)],[76]) ).
thf(464,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ A )
<=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__def) ).
thf(2231,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Oacyclic @ B @ A )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) )
& ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( 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)],[464]) ).
thf(370,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_Q____ ) @ c_Arrow__Order__Mirabelle_OProf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096Q_A_058_AProf_096) ).
thf(1856,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_Q____ ) @ c_Arrow__Order__Mirabelle_OProf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(477,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(2281,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(2282,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
inference(cnf,[status(esa)],[2281]) ).
thf(2807,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_Q____ ) @ c_Arrow__Order__Mirabelle_OProf ) )
!= ( hBOOL @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1856,2282]) ).
thf(2808,plain,
~ ( hBOOL @ ( hAPP @ c_fNot @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_Q____ ) @ c_Arrow__Order__Mirabelle_OProf ) ) ),
inference(pattern_uni,[status(thm)],[2807:[bind(A,$thf( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_Q____ ) @ c_Arrow__Order__Mirabelle_OProf ))]]) ).
thf(157,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 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__conv) ).
thf(994,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 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD2) ).
thf(2248,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
thf(873,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ E ) )
=> ( ( hAPP @ D @ G )
= ( hAPP @ C @ G ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ D ) @ ( c_FuncSet_OPi @ F @ B @ E @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ C ) @ ( c_FuncSet_OPi @ F @ B @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__cong) ).
thf(1269,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ E ) )
=> ( ( hAPP @ D @ G )
= ( hAPP @ C @ G ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ D ) @ ( c_FuncSet_OPi @ F @ B @ E @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ C ) @ ( c_FuncSet_OPi @ F @ B @ E @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ C ) @ ( c_FuncSet_OPi @ F @ B @ E @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ B ) ) @ D ) @ ( c_FuncSet_OPi @ F @ B @ E @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtranclE) ).
thf(878,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
thf(614,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)],[36]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',fact_empty__not__insert) ).
thf(582,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)],[26]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_Un__Int__assoc__eq) ).
thf(762,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( 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 )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(439,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_HOL_Obool ) @ ( c_Product__Type_OSigma @ C @ F @ B @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C @ D ) ) @ ( c_Product__Type_OSigma @ C @ F @ A @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C @ D ) ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__subset__cancel2) ).
thf(2099,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_HOL_Obool ) @ ( c_Product__Type_OSigma @ C @ F @ B @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C @ D ) ) @ ( c_Product__Type_OSigma @ C @ F @ A @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C @ D ) ) )
=> ( 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 ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_HOL_Obool ) @ ( c_Product__Type_OSigma @ C @ F @ B @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C @ D ) ) @ ( c_Product__Type_OSigma @ C @ F @ A @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(311,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_P____ @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_Q____ @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_J_096) ).
thf(1608,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_P____ @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_Q____ @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_Q____ @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_P____ @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
thf(550,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)],[15]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclp__rtrancl__eq) ).
thf(1735,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ D @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_prod @ D @ D ) ) @ ( tc_fun @ D @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ D ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ D @ ( c_member @ ( tc_prod @ D @ D ) ) ) ) @ ( c_Product__Type_OPair @ D @ D ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).
thf(1872,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Product__Type_OSigma @ D @ C @ B @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) )
<=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__empty) ).
thf(698,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Product__Type_OSigma @ D @ C @ B @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( c_Product__Type_OSigma @ D @ C @ B @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',fact_trancl__domain) ).
thf(747,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)],[82]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__subset) ).
thf(945,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(1954,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(420,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_inf1E) ).
thf(2042,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[420]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I5_J) ).
thf(1497,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_OPi @ E @ D @ B @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( c_FuncSet_Ocompose @ E @ E @ D @ B @ C @ ( c_FuncSet_Orestrict @ E @ E @ ( c_COMBI @ E ) @ B ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compose__Id) ).
thf(1705,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_OPi @ E @ D @ B @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( c_FuncSet_Ocompose @ E @ E @ D @ B @ C @ ( c_FuncSet_Orestrict @ E @ E @ ( c_COMBI @ E ) @ B ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
<=> ( ( C = B )
| ( ( C != B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
thf(1999,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C = B )
| ( ( C != B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ) )
& ( ( ( C = B )
| ( ( C != B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper1) ).
thf(797,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ F @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
thf(2316,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ F @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( C = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).
thf(1196,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( C = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI1) ).
thf(1746,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Oabove @ A ) @ C ) @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_above__Lin) ).
thf(2046,plain,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Oabove @ A ) @ C ) @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(514,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Predicate_ODomainP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) @ A )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Relation_ODomain @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).
thf(2432,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Predicate_ODomainP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Relation_ODomain @ D @ C @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Relation_ODomain @ D @ C @ B ) ) )
=> ( c_Predicate_ODomainP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Oacyclic @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) @ A ) )
<=> ( ( c_Wellfounded_Oacyclic @ D @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__insert) ).
thf(1441,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Oacyclic @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) @ A ) )
=> ( ( c_Wellfounded_Oacyclic @ D @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ B ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) )
& ( ( ( c_Wellfounded_Oacyclic @ D @ A )
& ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
<=> ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__Un) ).
thf(1613,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
=> ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) )
& ( ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
| ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( 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)],[312]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ A ) )
=> ( D != E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).
thf(1935,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ A ) )
=> ( D != E ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ A ) )
=> ( D != E ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( 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)],[397]) ).
thf(433,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 @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
thf(2082,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 @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD2) ).
thf(1724,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',fact_the__elem__eq) ).
thf(565,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)],[19]) ).
thf(380,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( 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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI) ).
thf(1887,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( 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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb2) ).
thf(651,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(494,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 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryD) ).
thf(2348,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 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
thf(1114,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(1115,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
inference(cnf,[status(esa)],[1114]) ).
thf(1116,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_COMBI @ B ) @ A )
= A ),
inference(lifteq,[status(thm)],[1115]) ).
thf(2570,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( hAPP @ ( c_COMBI @ B ) @ A )
!= ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) ) ),
inference(paramod_ordered,[status(thm)],[1116,519]) ).
thf(2590,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( c_COMBI @ B )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( A
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) ),
inference(simp,[status(thm)],[2570]) ).
thf(2619,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( c_COMBI @ A )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
inference(simp,[status(thm)],[2590]) ).
thf(2700,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ A )
| ( ( c_COMBI @ C )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( ( hAPP @ ( c_COMBI @ B ) @ A )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) @ ( hAPP @ v_F @ v_Q____ ) ) ) ),
inference(paramod_ordered,[status(thm)],[1116,2619]) ).
thf(2715,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ A )
| ( ( c_COMBI @ C )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( ( c_COMBI @ B )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) )
| ( A
!= ( hAPP @ v_F @ v_Q____ ) ) ),
inference(simp,[status(thm)],[2700]) ).
thf(2723,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ v_F @ v_Q____ ) )
| ( ( c_COMBI @ B )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( ( c_COMBI @ A )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) ),
inference(simp,[status(thm)],[2715]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ C ) @ B ) @ A ) ) )
=> ( hBOOL @ ( c_Product__Type_Ocurry @ D @ C @ tc_HOL_Obool @ E @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryI) ).
thf(973,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ ( hAPP @ ( hAPP @ ( 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)],[151]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).
thf(885,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(293,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complete__Lin) ).
thf(1529,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( 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)],[293]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_le__infE) ).
thf(1967,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__absorb) ).
thf(2039,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(71,axiom,
! [A: $i,B: $i] : ( c_Relation_Osingle__valued @ B @ B @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
thf(718,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)],[71]) ).
thf(719,plain,
! [B: $i,A: $i] : ( c_Relation_Osingle__valued @ B @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(cnf,[status(esa)],[718]) ).
thf(93,axiom,
class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
thf(785,plain,
class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(518,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ORange @ C @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Relation_ORange @ C @ D @ B ) ) @ ( c_Relation_ORange @ C @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Int__subset) ).
thf(2444,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ORange @ C @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Relation_ORange @ C @ D @ B ) ) @ ( c_Relation_ORange @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_Diff__partition) ).
thf(619,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( 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)],[38]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_Oextensional__funcset @ F @ E @ C @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( hAPP @ D @ A )
= ( c_HOL_Oundefined @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__funcset__arb) ).
thf(2274,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_Oextensional__funcset @ F @ E @ C @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( hAPP @ D @ A )
= ( c_HOL_Oundefined @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__mem) ).
thf(1279,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ B ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ A @ C @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_below__Lin) ).
thf(934,plain,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ A @ C @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel) ).
thf(2126,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(191,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/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
thf(1132,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)],[191]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).
thf(949,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Omlex__prod @ C @ B @ A )
= ( c_Relation_Oinv__image @ ( tc_prod @ tc_Nat_Onat @ C ) @ C @ ( c_Wellfounded_Olex__prod @ tc_Nat_Onat @ C @ c_Wellfounded_Oless__than @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ C @ ( tc_prod @ tc_Nat_Onat @ C ) ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ C @ ( tc_prod @ tc_Nat_Onat @ C ) ) @ C @ ( c_Product__Type_OPair @ tc_Nat_Onat @ C ) ) @ B ) ) @ ( c_COMBI @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__prod__def) ).
thf(2185,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Omlex__prod @ C @ B @ A )
= ( c_Relation_Oinv__image @ ( tc_prod @ tc_Nat_Onat @ C ) @ C @ ( c_Wellfounded_Olex__prod @ tc_Nat_Onat @ C @ c_Wellfounded_Oless__than @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ C @ ( tc_prod @ tc_Nat_Onat @ C ) ) @ ( hAPP @ ( c_COMBB @ tc_Nat_Onat @ ( tc_fun @ C @ ( tc_prod @ tc_Nat_Onat @ C ) ) @ C @ ( c_Product__Type_OPair @ tc_Nat_Onat @ C ) ) @ B ) ) @ ( c_COMBI @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(304,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
thf(1577,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[304]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rtrancl__UnI) ).
thf(1922,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( hAPP @ ( hAPP @ ( 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)],[392]) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(638,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)],[44]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ C ) @ E ) @ B ) ) @ ( c_Product__Type_OSigma @ F @ C @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaI) ).
thf(1379,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ C ) @ E ) @ B ) ) @ ( c_Product__Type_OSigma @ F @ C @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ ( hAPP @ B @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PiE) ).
thf(1147,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ ( hAPP @ B @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_singletonE) ).
thf(969,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[150]) ).
thf(2571,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ A )
| ( ( hAPP @ ( c_COMBI @ B ) @ A )
!= ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_Q____ ) ) ) ),
inference(paramod_ordered,[status(thm)],[1116,519]) ).
thf(2606,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ A )
| ( ( c_COMBI @ B )
!= ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) )
| ( A
!= ( hAPP @ v_F @ v_Q____ ) ) ),
inference(simp,[status(thm)],[2571]) ).
thf(2635,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ v_F @ v_Q____ ) )
| ( ( c_COMBI @ A )
!= ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) ) ),
inference(simp,[status(thm)],[2606]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ C ) ) @ ( c_FuncSet_Orestrict @ D @ C @ B @ A ) ) @ ( c_FuncSet_Oextensional @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__extensional) ).
thf(1847,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ C ) ) @ ( c_FuncSet_Orestrict @ D @ C @ B @ A ) ) @ ( c_FuncSet_Oextensional @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(508,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Ototal__on @ C @ B @ A )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ E ) ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ E ) @ D ) ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__def) ).
thf(2403,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Ototal__on @ C @ B @ A )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ E ) ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ E ) @ D ) ) @ A ) ) ) ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ E ) @ B ) )
=> ( ( D != E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ E ) ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ E ) @ D ) ) @ A ) ) ) ) ) )
=> ( c_Relation_Ototal__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_FuncSet_OPi @ D @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ D @ C ) @ tc_HOL_Obool ) ) )
<=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__eq__empty) ).
thf(1087,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_FuncSet_OPi @ D @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ D @ C ) @ tc_HOL_Obool ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
& ( ( hAPP @ A @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( c_FuncSet_OPi @ D @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ D @ C ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__mono) ).
thf(1514,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ D ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__rtranclp) ).
thf(1247,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ D ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(422,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq) ).
thf(2049,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge2) ).
thf(1319,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).
thf(870,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Product__Type_OSigma @ E @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ A ) ) @ ( c_Product__Type_OSigma @ E @ D @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib1) ).
thf(2301,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Product__Type_OSigma @ E @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ A ) ) @ ( c_Product__Type_OSigma @ E @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ F ) @ A ) @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I1) ).
thf(1815,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ F ) @ A ) @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Relation_OId__on @ D @ A ) ) )
<=> ( ( C = B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__iff) ).
thf(2222,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Relation_OId__on @ D @ A ) ) )
=> ( ( C = B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( C = B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Relation_OId__on @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
<=> ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).
thf(1489,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( 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] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(318,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ODomain @ D @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
thf(1664,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ODomain @ D @ D @ B ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
=> ( C = A ) )
& ( ( C = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(335,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__sup @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ B ) @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oidem) ).
thf(1714,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__sup @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ B ) @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( hAPP @ ( c_FuncSet_Ocompose @ G @ D @ C @ E @ B @ A ) @ F )
= ( hAPP @ B @ ( hAPP @ A @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compose__eq) ).
thf(1373,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( hAPP @ ( c_FuncSet_Ocompose @ G @ D @ C @ E @ B @ A ) @ F )
= ( hAPP @ B @ ( hAPP @ A @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D @ C @ A ) ) @ B )
= ( c_Set_Oinsert @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D @ C @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left) ).
thf(1136,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D @ C @ A ) ) @ B )
= ( c_Set_Oinsert @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D @ C @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).
thf(2122,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(406,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/sandbox/benchmark/theBenchmark.p',fact_Domain__empty) ).
thf(1978,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)],[406]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Ocommute) ).
thf(937,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(237,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/sandbox/benchmark/theBenchmark.p',fact_mono__Field) ).
thf(1283,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)],[237]) ).
thf(436,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I3_J) ).
thf(2090,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(29,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 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__least) ).
thf(591,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 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(269,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortranclp @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) @ c_fequal ) )
= ( c_Transitive__Closure_Ortranclp @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclp__reflcl) ).
thf(1418,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortranclp @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) @ c_fequal ) )
= ( c_Transitive__Closure_Ortranclp @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ G ) @ F ) ) @ A ) )
=> ( G = F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).
thf(2236,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ G ) @ F ) ) @ A ) )
=> ( G = F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib) ).
thf(623,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Osimps) ).
thf(1677,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(417,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Un) ).
thf(2034,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( 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)],[417]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntE) ).
thf(1581,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(149,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 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__def) ).
thf(966,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 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D @ C @ B ) ) @ A )
= ( c_Set_Oinsert @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__left) ).
thf(692,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D @ C @ B ) ) @ A )
= ( c_Set_Oinsert @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(379,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_P_H____ ) @ c_Arrow__Order__Mirabelle_OProf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096P_H_A_058_AProf_096) ).
thf(1886,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_P_H____ ) @ c_Arrow__Order__Mirabelle_OProf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(352,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B @ ( c_Product__Type_OSigma @ E @ E @ A @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ E @ A ) ) )
=> ( ( D = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma__aux) ).
thf(1796,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B @ ( c_Product__Type_OSigma @ E @ E @ A @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ E @ A ) ) )
=> ( ( D = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_le__inf__iff) ).
thf(1351,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(52,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Relation_OId__on @ B @ A ) @ ( c_Product__Type_OSigma @ B @ B @ A @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__subset__Times) ).
thf(660,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Relation_OId__on @ B @ A ) @ ( c_Product__Type_OSigma @ B @ B @ A @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) @ B ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
thf(1201,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( 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)],[213]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq) ).
thf(1242,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ D ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(6,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 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__mono) ).
thf(526,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 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(527,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $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 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(cnf,[status(esa)],[526]) ).
thf(328,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(1696,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( 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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).
thf(1169,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( 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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ K ) @ L ) ) @ ( hAPP @ ( hAPP @ ( 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)],[205]) ).
thf(63,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 @ ( tc_fun @ E @ B ) @ tc_HOL_Obool ) @ ( c_FuncSet_OPi @ E @ B @ C @ A ) @ ( c_FuncSet_OPi @ E @ B @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
thf(687,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 @ ( tc_fun @ E @ B ) @ tc_HOL_Obool ) @ ( c_FuncSet_OPi @ E @ B @ C @ A ) @ ( c_FuncSet_OPi @ E @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(515,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D2) ).
thf(2437,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
thf(1928,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Wellfounded_Oacc @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
thf(1447,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Wellfounded_Oacc @ D @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Ocommute) ).
thf(956,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(511,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(2424,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Id__on) ).
thf(774,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)],[88]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ A @ C ) )
=> ( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ G ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__induct) ).
thf(2371,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ A @ C ) )
=> ( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ G ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( 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)],[500]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__commute) ).
thf(2242,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',fact_Field__empty) ).
thf(1345,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)],[253]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) @ E @ D )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ E ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ B @ G ) @ ( hAPP @ A @ G ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ C ) @ tc_HOL_Obool ) @ ( c_Product__Type_OSigma @ F @ C @ E @ B ) @ ( c_Product__Type_OSigma @ F @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__mono) ).
thf(988,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) @ E @ D )
=> ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ G ) @ E ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ B @ G ) @ ( hAPP @ A @ G ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ C ) @ tc_HOL_Obool ) @ ( c_Product__Type_OSigma @ F @ C @ E @ B ) @ ( c_Product__Type_OSigma @ F @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I6_J) ).
thf(1975,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(301,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/sandbox/benchmark/theBenchmark.p',fact_bot__fun__def) ).
thf(1564,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)],[301]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
<=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__sup) ).
thf(1074,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( 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)],[175]) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
thf(1206,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)],[215]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__absorb) ).
thf(942,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
thf(2204,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBB @ F @ E @ D @ C ) @ B ) @ A )
= ( hAPP @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(2470,plain,
! [A: $i] :
( ~ ( hBOOL @ A )
| ( ( hBOOL @ ( hAPP @ c_fNot @ A ) )
!= ( hBOOL @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2282]) ).
thf(2473,plain,
! [A: $i] :
( ~ ( hBOOL @ A )
| ( ( hAPP @ c_fNot @ A )
!= A ) ),
inference(simp,[status(thm)],[2470]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= C )
=> ( ( c_Fun_Ofun__upd @ B @ A @ E @ D @ C )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__idem) ).
thf(925,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hAPP @ E @ D )
= C )
=> ( ( c_Fun_Ofun__upd @ B @ A @ E @ D @ C )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ ( c_FuncSet_Orestrict @ E @ C @ B @ D ) ) @ ( c_FuncSet_OPi @ E @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__in__funcset) ).
thf(1306,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ ( c_FuncSet_Orestrict @ E @ C @ B @ D ) ) @ ( c_FuncSet_OPi @ E @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(105,axiom,
class_Lattices_Odistrib__lattice @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Odistrib__lattice) ).
thf(810,plain,
class_Lattices_Odistrib__lattice @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',fact_trancl__range) ).
thf(532,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)],[10]) ).
thf(533,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Relation_ORange @ B @ B @ A ) ),
inference(cnf,[status(esa)],[532]) ).
thf(534,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Relation_ORange @ B @ B @ A ) ),
inference(lifteq,[status(thm)],[533]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',fact_insert__not__empty) ).
thf(714,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)],[70]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Relation_ORange @ E @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeI) ).
thf(2061,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ B ) @ ( c_Relation_ORange @ E @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(8,axiom,
class_Orderings_Oord @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(529,plain,
class_Orderings_Oord @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
thf(1691,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(12,axiom,
class_Lattices_Olattice @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
thf(546,plain,
class_Lattices_Olattice @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(97,axiom,
v_a_H____ != v_b_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d1_I2_J) ).
thf(793,plain,
v_a_H____ != v_b_H____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Ofun__upd @ D @ C @ B @ A @ ( hAPP @ B @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
thf(1915,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Fun_Ofun__upd @ D @ C @ B @ A @ ( hAPP @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).
thf(1708,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ C @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C @ ( c_COMBB @ ( tc_prod @ C @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ C @ C ) ) ) ) @ ( c_Product__Type_OPair @ C @ C ) ) ) ) @ B ) ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__acc__eq) ).
thf(1047,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ C @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C @ ( c_COMBB @ ( tc_prod @ C @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ C @ C ) ) ) ) @ ( c_Product__Type_OPair @ C @ C ) ) ) ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ C @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ C @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ C @ ( c_COMBB @ ( tc_prod @ C @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ C @ C ) ) ) ) @ ( c_Product__Type_OPair @ C @ C ) ) ) ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( c_Relation_OField @ B @ A )
= ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_Field__def) ).
thf(1730,plain,
! [A: $i,B: $i] :
( ( c_Relation_OField @ B @ A )
= ( hAPP @ ( hAPP @ ( 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)],[341]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(1021,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
thf(1519,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) )
=> ( 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 ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__fun__def) ).
thf(1255,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(119,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ B ) @ ( c_Orderings_Obot__class_Obot @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__left) ).
thf(862,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ B ) @ ( c_Orderings_Obot__class_Obot @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Product__Type_OSigma @ E @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) @ ( c_Product__Type_OSigma @ E @ D @ B @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Un__distrib1) ).
thf(1217,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Product__Type_OSigma @ E @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) @ ( c_Product__Type_OSigma @ E @ D @ B @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
thf(1487,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ B @ E ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ B @ E ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtranclp__into__rtranclp) ).
thf(2032,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ B @ E ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ B @ E ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ G @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ C ) ) ) @ ( c_Recdef_Osame__fst @ A @ E @ G @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
thf(2396,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ G @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ A @ E ) @ F ) @ C ) ) ) @ ( c_Recdef_Osame__fst @ A @ E @ G @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(414,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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ H ) @ B ) ) @ D ) )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ H @ ( hAPP @ G @ H ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Osimps) ).
thf(2015,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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( 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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( 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)],[414]) ).
thf(265,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/sandbox/benchmark/theBenchmark.p',fact_Domain__mono) ).
thf(1387,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)],[265]) ).
thf(385,axiom,
v_b____ != v_a_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d2_I2_J) ).
thf(1900,plain,
v_b____ != v_a_H____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ C ) @ ( c_Product__Type_OSigma @ E @ D @ B @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ B ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ G ) @ ( hAPP @ A @ F ) ) )
=> ( C
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ F ) @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE) ).
thf(910,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ C ) @ ( c_Product__Type_OSigma @ E @ D @ B @ A ) ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ B ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ G ) @ ( hAPP @ A @ F ) ) )
=> ( C
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ F ) @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(111,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset__conv) ).
thf(825,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 @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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)],[111]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
thf(1343,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclE) ).
thf(1355,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(475,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__mono) ).
thf(2277,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(303,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/sandbox/benchmark/theBenchmark.p',fact_Range__empty__iff) ).
thf(1570,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)],[303]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FuncSet_Oextensional__funcset @ D @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ D @ C ) @ tc_HOL_Obool ) ) @ ( c_FuncSet_OPi @ D @ C @ B @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D @ A ) ) ) @ ( c_FuncSet_Oextensional @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__funcset__def) ).
thf(1174,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FuncSet_Oextensional__funcset @ D @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_fun @ D @ C ) @ tc_HOL_Obool ) ) @ ( c_FuncSet_OPi @ D @ C @ B @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ D @ A ) ) ) @ ( c_FuncSet_Oextensional @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
thf(788,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)],[95]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ C ) ) @ B ) @ ( c_FuncSet_Oextensional @ D @ C @ A ) ) )
=> ( ( c_FuncSet_Orestrict @ D @ C @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__restrict) ).
thf(1370,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ C ) ) @ B ) @ ( c_FuncSet_Oextensional @ D @ C @ A ) ) )
=> ( ( c_FuncSet_Orestrict @ D @ C @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(447,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( 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 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ D ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ A ) ) @ C ) ) ) )
& ( ( B != E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__below) ).
thf(2132,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( 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 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ D ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ A ) ) @ C ) ) ) )
& ( ( B != E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) )
& ( ( ( B != A )
& ( ( A = E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ D ) ) @ C ) ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ A ) ) @ C ) ) ) )
& ( ( B != E )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( 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)],[447]) ).
thf(75,axiom,
class_Lattices_Osemilattice__sup @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
thf(729,plain,
class_Lattices_Osemilattice__sup @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Relation_ODomain @ D @ C @ B ) ) @ ( c_Relation_ODomain @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).
thf(1423,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( 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)],[271]) ).
thf(2455,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ A @ v_b____ ) ) @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A )
!= ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) ) ),
inference(paramod_ordered,[status(thm)],[525,519]) ).
thf(2458,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ A @ v_b____ ) ) @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
!= ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A != v_a____ ) ),
inference(simp,[status(thm)],[2455]) ).
thf(2464,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ v_a____ @ v_b____ ) ) @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
!= ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(simp,[status(thm)],[2458]) ).
thf(362,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Transitive__Closure_Ortrancl @ C @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__rtrancl) ).
thf(1837,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Transitive__Closure_Ortrancl @ C @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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)],[362]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Recdef_Oadm__wf @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ C ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ D @ C ) @ ( c_COMBS @ D @ D @ C ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ D @ C ) @ ( c_COMBB @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ C ) @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ C ) @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) ) @ ( c_Recdef_Ocut @ D @ C ) ) @ B ) ) ) ) @ ( c_COMBI @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_adm__lemma) ).
thf(1920,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Recdef_Oadm__wf @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ C ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ ( tc_fun @ D @ D ) @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ D @ C ) @ ( c_COMBS @ D @ D @ C ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) @ ( tc_fun @ D @ C ) @ ( c_COMBB @ ( tc_fun @ D @ C ) @ ( tc_fun @ D @ C ) @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ D @ C ) @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ ( tc_fun @ D @ ( tc_fun @ D @ C ) ) ) @ ( c_Recdef_Ocut @ D @ C ) ) @ B ) ) ) ) @ ( c_COMBI @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).
thf(852,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)],[115]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__commute) ).
thf(1951,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(128,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/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(889,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)],[128]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I8_J) ).
thf(1159,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Product__Type_OSigma @ E @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) @ ( c_Product__Type_OSigma @ E @ D @ B @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__Int__distrib1) ).
thf(2345,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Product__Type_OSigma @ E @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) @ ( c_Product__Type_OSigma @ E @ D @ B @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2E) ).
thf(2313,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD2) ).
thf(1281,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice @ B )
=> ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
thf(521,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice @ B )
=> ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(522,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ B )
| ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) ) ),
inference(cnf,[status(esa)],[521]) ).
thf(112,axiom,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ A @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).
thf(830,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)],[112]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_OField @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_Field__Un) ).
thf(1079,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_OField @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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)],[176]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ B @ A ) ) )
<=> ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(1027,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ B @ A ) ) )
=> ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(441,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D1) ).
thf(2112,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(710,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)],[69]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C = B )
| ( ( C != B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclD) ).
thf(1740,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( ( C = B )
| ( ( C != B )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ORange @ B @ D @ A ) ) )
=> ~ ! [E: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ D ) @ E ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeE) ).
thf(1910,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ORange @ B @ D @ A ) ) )
=> ~ ! [E: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ D ) @ E ) @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(294,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__left__idem) ).
thf(1534,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ A ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ B ) )
=> ( ( hAPP @ C @ F )
= ( hAPP @ A @ F ) ) )
=> ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensionalityI) ).
thf(1328,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ A ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ B ) )
=> ( ( hAPP @ C @ F )
= ( hAPP @ A @ F ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(1064,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__assoc) ).
thf(1425,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).
thf(593,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)],[30]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Product__Type_OSigma @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ B ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib2) ).
thf(1360,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Product__Type_OSigma @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ B ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).
thf(2245,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
<=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__Un) ).
thf(1592,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
=> ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) ) )
& ( ( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( 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)],[310]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortranclp @ C @ B ) @ ( c_Transitive__Closure_Ortranclp @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclp__mono) ).
thf(578,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( c_Transitive__Closure_Ortranclp @ C @ B ) @ ( c_Transitive__Closure_Ortranclp @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mem) ).
thf(1143,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_OPi @ F @ E @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( c_HOL_Oundefined @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__apply) ).
thf(2115,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( c_HOL_Oundefined @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Osemilattice__inf @ 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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__mono) ).
thf(1851,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Osemilattice__inf @ 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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(351,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
<=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ F ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ F ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IIA__def) ).
thf(1772,plain,
! [A: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ A )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ F ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ F ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ B ) ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ F ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ F ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ A @ B ) ) ) ) ) ) ) )
=> ( c_Arrow__Order__Mirabelle_OIIA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
<=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(1970,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) ) )
& ( ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) )
=> ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ K @ J ) ) @ I ) @ ( c_FuncSet_OPi @ K @ J @ H @ ( c_COMBK @ ( tc_fun @ J @ tc_HOL_Obool ) @ K @ G ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ J @ F ) ) @ E ) @ ( c_FuncSet_OPi @ J @ F @ G @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ J @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ C ) ) @ B ) @ ( c_FuncSet_OPi @ F @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ F @ A ) ) ) )
=> ( ( c_FuncSet_Ocompose @ K @ F @ C @ H @ B @ ( c_FuncSet_Ocompose @ K @ J @ F @ H @ E @ I ) )
= ( c_FuncSet_Ocompose @ K @ J @ C @ H @ ( c_FuncSet_Ocompose @ J @ F @ C @ G @ B @ E ) @ I ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compose__assoc) ).
thf(1227,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ K @ J ) ) @ I ) @ ( c_FuncSet_OPi @ K @ J @ H @ ( c_COMBK @ ( tc_fun @ J @ tc_HOL_Obool ) @ K @ G ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ J @ F ) ) @ E ) @ ( c_FuncSet_OPi @ J @ F @ G @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ J @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ C ) ) @ B ) @ ( c_FuncSet_OPi @ F @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ F @ A ) ) ) )
=> ( ( c_FuncSet_Ocompose @ K @ F @ C @ H @ B @ ( c_FuncSet_Ocompose @ K @ J @ F @ H @ E @ I ) )
= ( c_FuncSet_Ocompose @ K @ J @ C @ H @ ( c_FuncSet_Ocompose @ J @ F @ C @ G @ B @ E ) @ I ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(74,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/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
thf(725,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)],[74]) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',fact_trancl__empty) ).
thf(980,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)],[153]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
thf(1587,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).
thf(1096,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).
thf(1672,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(2701,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( c_COMBI @ C )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( ( hAPP @ ( c_COMBI @ B ) @ A )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) ),
inference(paramod_ordered,[status(thm)],[1116,2619]) ).
thf(2716,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( c_COMBI @ C )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( ( c_COMBI @ B )
!= ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) )
| ( A != v_b____ ) ),
inference(simp,[status(thm)],[2701]) ).
thf(2724,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ v_b____ @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( c_COMBI @ B )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( ( c_COMBI @ A )
!= ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) ) ),
inference(simp,[status(thm)],[2716]) ).
thf(337,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/sandbox/benchmark/theBenchmark.p',fact_refl__on__empty) ).
thf(1719,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)],[337]) ).
thf(302,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__distrib2) ).
thf(1567,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Nitpick_Owf__wfrec_H @ E @ D @ C @ B @ A )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ E @ D ) @ ( c_Nitpick_Owf__wfrec @ E @ D @ C @ B ) ) @ C ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Owf__wfrec_H__def) ).
thf(1082,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Nitpick_Owf__wfrec_H @ E @ D @ C @ B @ A )
= ( hAPP @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ E @ D ) @ ( c_Nitpick_Owf__wfrec @ E @ D @ C @ B ) ) @ C ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcsetI) ).
thf(1964,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib2) ).
thf(642,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_ODomain @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_Domain__Un__eq) ).
thf(1584,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_ODomain @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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)],[307]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Set_Oinsert @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
thf(1700,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Set_Oinsert @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclicI) ).
thf(1214,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( 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)],[218]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Predicate_ORangeP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) @ A )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Relation_ORange @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).
thf(1889,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Predicate_ORangeP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Relation_ORange @ D @ C @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ A ) @ ( c_Relation_ORange @ D @ C @ B ) ) )
=> ( c_Predicate_ORangeP @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__apply) ).
thf(2196,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(364,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 @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
thf(1842,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 @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(2472,plain,
! [A: $i] :
( ~ ( hBOOL @ A )
| ( ( hBOOL @ ( hAPP @ c_fNot @ A ) )
!= ( hBOOL @ A ) ) ),
inference(simp,[status(thm)],[2470]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D @ C @ B ) ) @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Set_Oinsert @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__inter__insert) ).
thf(679,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D @ C @ B ) ) @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Set_Oinsert @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( c_Relation_ODomain @ E @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainI) ).
thf(1155,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( c_Relation_ODomain @ E @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(13,axiom,
class_Orderings_Oord @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(547,plain,
class_Orderings_Oord @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(39,axiom,
class_Lattices_Osemilattice__inf @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
thf(622,plain,
class_Lattices_Osemilattice__inf @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D @ C @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if0) ).
thf(1249,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D @ C @ A ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(484,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( ( ( c_Set_Oinsert @ D @ C @ B )
= ( c_Set_Oinsert @ D @ C @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(2304,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[484]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortranclp @ B @ ( c_Transitive__Closure_Ortranclp @ B @ A ) )
= ( c_Transitive__Closure_Ortranclp @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclp__idemp) ).
thf(654,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortranclp @ B @ ( c_Transitive__Closure_Ortranclp @ B @ A ) )
= ( c_Transitive__Closure_Ortranclp @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2E) ).
thf(1192,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
thf(1799,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ C @ A )
= ( c_HOL_Oundefined @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__arb) ).
thf(1984,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ C @ A )
= ( c_HOL_Oundefined @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(159,axiom,
v_a____ != v_b_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d2_I1_J) ).
thf(1000,plain,
v_a____ != v_b_H____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(1001,plain,
v_a____ != v_b_H____,
inference(polarity_switch,[status(thm)],[1000]) ).
thf(1002,plain,
v_b_H____ != v_a____,
inference(lifteq,[status(thm)],[1001]) ).
thf(375,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oidem) ).
thf(1874,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oirrefl @ B @ A )
<=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__def) ).
thf(1429,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Oirrefl @ B @ A )
=> ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) ) )
& ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) )
=> ( c_Relation_Oirrefl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(3,axiom,
class_Lattices_Obounded__lattice @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).
thf(520,plain,
class_Lattices_Obounded__lattice @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2448,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ( ( class_Lattices_Obounded__lattice @ tc_HOL_Obool )
!= ( class_Lattices_Obounded__lattice @ B ) ) ),
inference(paramod_ordered,[status(thm)],[520,522]) ).
thf(2449,plain,
! [A: $i] : ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ tc_HOL_Obool ) ),
inference(pattern_uni,[status(thm)],[2448:[bind(A,$thf( A )),bind(B,$thf( tc_HOL_Obool ))]]) ).
thf(2480,plain,
! [C: $i,B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ B @ C ) )
| ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ tc_HOL_Obool ) )
!= ( class_Lattices_Obounded__lattice @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2449,522]) ).
thf(2481,plain,
! [B: $i,A: $i] : ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(pattern_uni,[status(thm)],[2480:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_fun @ D @ tc_HOL_Obool ))]]) ).
thf(2482,plain,
! [B: $i,A: $i] : ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(simp,[status(thm)],[2481]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ ( c_Product__Type_OSigma @ C @ C @ A @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( c_Product__Type_OSigma @ C @ C @ A @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__subset__Sigma) ).
thf(779,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ ( c_Product__Type_OSigma @ C @ C @ A @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( c_Product__Type_OSigma @ C @ C @ A @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
thf(605,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)],[34]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( 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 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mkbot) ).
thf(1627,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( 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 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( 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 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( 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)],[313]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oleft__idem) ).
thf(2285,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(47,axiom,
class_Lattices_Osemilattice__inf @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
thf(647,plain,
class_Lattices_Osemilattice__inf @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__same) ).
thf(1263,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ E @ D @ C @ B @ A ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__left__commute) ).
thf(997,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ ( c_Orderings_Obot__class_Obot @ B ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__bot__left) ).
thf(1266,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ ( c_Orderings_Obot__class_Obot @ B ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__I) ).
thf(2387,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(250,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/sandbox/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).
thf(1333,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)],[250]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_FuncSet_Oextensional__funcset @ B @ A @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__funcset__empty__range) ).
thf(633,plain,
! [A: $i,B: $i,C: $i] :
( ( C
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( ( c_FuncSet_Oextensional__funcset @ B @ A @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower2) ).
thf(805,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(535,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)],[11]) ).
thf(536,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 ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( 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(miniscope,[status(thm)],[535]) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( 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(cnf,[status(esa)],[536]) ).
thf(540,plain,
! [C: $i,B: $i,A: $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(lifteq,[status(thm)],[537]) ).
thf(541,plain,
! [C: $i,B: $i,A: $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(simp,[status(thm)],[540]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ G @ B ) @ F @ A )
= ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ F @ A ) @ G @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__twist) ).
thf(657,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G != F )
=> ( ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ G @ B ) @ F @ A )
= ( c_Fun_Ofun__upd @ E @ D @ ( c_Fun_Ofun__upd @ E @ D @ C @ F @ A ) @ G @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) @ F ) @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2I2) ).
thf(1712,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) @ F ) @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(431,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ ( c_Product__Type_OSigma @ C @ C @ A @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C @ A ) ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) @ B ) ) )
=> ( c_Relation_Orefl__on @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onI) ).
thf(2076,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ ( c_Product__Type_OSigma @ C @ C @ A @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C @ A ) ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) @ B ) ) )
=> ( c_Relation_Orefl__on @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__absorb) ).
thf(2368,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
thf(558,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)],[18]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
thf(530,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)],[9]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( 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/sandbox/benchmark/theBenchmark.p',fact_Int__empty__left) ).
thf(586,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( 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)],[27]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downward) ).
thf(1434,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(371,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/sandbox/benchmark/theBenchmark.p',fact_single__valued__subset) ).
thf(1857,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)],[371]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__downward) ).
thf(1187,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(516,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ H @ G ) ) @ F ) @ ( c_FuncSet_OPi @ H @ G @ E @ ( c_COMBK @ ( tc_fun @ G @ tc_HOL_Obool ) @ H @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ C ) ) @ B ) @ ( c_FuncSet_OPi @ G @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ G @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ H @ C ) ) @ ( c_FuncSet_Ocompose @ H @ G @ C @ E @ B @ F ) ) @ ( c_FuncSet_OPi @ H @ C @ E @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ H @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__compose) ).
thf(2440,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ H @ G ) ) @ F ) @ ( c_FuncSet_OPi @ H @ G @ E @ ( c_COMBK @ ( tc_fun @ G @ tc_HOL_Obool ) @ H @ D ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ G @ C ) ) @ B ) @ ( c_FuncSet_OPi @ G @ C @ D @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ G @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ H @ C ) ) @ ( c_FuncSet_Ocompose @ H @ G @ C @ E @ B @ F ) ) @ ( c_FuncSet_OPi @ H @ C @ E @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ H @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(53,axiom,
class_Orderings_Obot @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
thf(662,plain,
class_Orderings_Obot @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( 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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ! [K: $i,L: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).
thf(1103,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( 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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) ) )
=> ! [K: $i,L: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ I ) @ J ) ) @ ( hAPP @ ( hAPP @ ( 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)],[183]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Obounded__lattice__bot @ C )
=> ( ( ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_sup__eq__bot__iff) ).
thf(1548,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Obounded__lattice__bot @ C )
=> ( ( ( ( hAPP @ ( hAPP @ ( 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 ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__commute) ).
thf(856,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oleft__commute) ).
thf(1301,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__Int) ).
thf(573,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( 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 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb2) ).
thf(689,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(501,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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ H ) @ B ) ) @ D ) )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ H @ ( hAPP @ G @ H ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Oequations) ).
thf(2376,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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( 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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( 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)],[501]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',fact_Diff__insert) ).
thf(733,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)],[77]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',fact_less__by__empty) ).
thf(601,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)],[33]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_Un__empty) ).
thf(750,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( 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 ) ) ) )
=> ( ( hAPP @ ( hAPP @ ( 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)],[83]) ).
thf(340,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__commute) ).
thf(1727,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(109,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__right) ).
thf(819,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ A @ D ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ G ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ F ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__induct) ).
thf(975,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ A @ D ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( 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)],[152]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( 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 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mktop) ).
thf(1389,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( 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 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( 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 )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ C ) ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( 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)],[266]) ).
thf(315,axiom,
! [A: $i] :
( ~ ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(1652,plain,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(80,axiom,
class_Orderings_Obot @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
thf(743,plain,
class_Orderings_Obot @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(506,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortranclp @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ B @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ B @ c_fNot ) ) @ c_fequal ) ) )
= ( c_Transitive__Closure_Ortranclp @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclp__r__diff__Id) ).
thf(2398,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortranclp @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) @ A ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( tc_fun @ B @ tc_HOL_Obool ) @ B @ ( c_COMBB @ tc_HOL_Obool @ tc_HOL_Obool @ B @ c_fNot ) ) @ c_fequal ) ) )
= ( c_Transitive__Closure_Ortranclp @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ ( c_FuncSet_Orestrict @ E @ C @ B @ D ) ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrictI) ).
thf(2188,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ ( c_FuncSet_Orestrict @ E @ C @ B @ D ) ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice @ B )
=> ( class_Lattices_Obounded__lattice__bot @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).
thf(772,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice @ B )
=> ( class_Lattices_Obounded__lattice__bot @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(504,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ B @ F ) @ ( hAPP @ A @ F ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ E @ C ) @ tc_HOL_Obool ) @ ( c_FuncSet_OPi @ E @ C @ D @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mono) ).
thf(2393,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ B @ F ) @ ( hAPP @ A @ F ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_fun @ E @ C ) @ tc_HOL_Obool ) @ ( c_FuncSet_OPi @ E @ C @ D @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ G ) ) @ A ) )
=> ( F = G ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separatorE) ).
thf(1752,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
=> ( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ F ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ F ) @ G ) ) @ A ) )
=> ( F = G ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(273,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_P____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096) ).
thf(1428,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_F @ v_P____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_COMBK @ D @ C @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
thf(2193,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_COMBK @ D @ C @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
thf(571,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)],[21]) ).
thf(572,plain,
! [B: $i,A: $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(cnf,[status(esa)],[571]) ).
thf(481,axiom,
! [A: $i,B: $i] :
( ( c_Nitpick_Orefl_H @ B @ A )
<=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
thf(2293,plain,
! [A: $i,B: $i] :
( ( ( c_Nitpick_Orefl_H @ B @ A )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) ) )
& ( ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ C ) @ C ) ) @ A ) )
=> ( c_Nitpick_Orefl_H @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(244,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI) ).
thf(1312,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(373,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(1865,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I2) ).
thf(1733,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ORange @ E @ D @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( c_Relation_ORange @ E @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__insert) ).
thf(1058,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ORange @ E @ D @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) @ ( hAPP @ ( hAPP @ ( 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)],[171]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ B ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
thf(1997,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ B ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(517,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distrib__sup__le) ).
thf(2442,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) @ B ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
thf(1258,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 )
=> ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) @ B ) ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A ) @ B ) ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( 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)],[230]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ E @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ E @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclp_Ortrancl__into__rtrancl) ).
thf(947,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ E @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ E @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).
thf(1224,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(321,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ D @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__downwards) ).
thf(1675,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ D @ C ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(383,axiom,
c_Arrow__Order__Mirabelle_OIIA @ v_F,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I3_J) ).
thf(1897,plain,
c_Arrow__Order__Mirabelle_OIIA @ v_F,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(2555,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ C @ D ) )
| ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
!= ( class_Lattices_Obounded__lattice @ D ) ) ),
inference(paramod_ordered,[status(thm)],[2482,522]) ).
thf(2556,plain,
! [C: $i,B: $i,A: $i] : ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ ( tc_fun @ B @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
inference(pattern_uni,[status(thm)],[2555:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( tc_fun @ E @ ( tc_fun @ G @ tc_HOL_Obool ) ))]]) ).
thf(2557,plain,
! [C: $i,B: $i,A: $i] : ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ ( tc_fun @ B @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
inference(simp,[status(thm)],[2556]) ).
thf(2698,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) @ A ) )
| ( ( c_COMBI @ C )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( ( hAPP @ ( c_COMBI @ B ) @ A )
!= ( hAPP @ v_F @ v_Q____ ) ) ),
inference(paramod_ordered,[status(thm)],[1116,2619]) ).
thf(2713,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) @ A ) )
| ( ( c_COMBI @ C )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( ( c_COMBI @ B )
!= v_F )
| ( A != v_Q____ ) ),
inference(simp,[status(thm)],[2698]) ).
thf(2721,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) @ v_Q____ ) )
| ( ( c_COMBI @ B )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( ( c_COMBI @ A )
!= v_F ) ),
inference(simp,[status(thm)],[2713]) ).
thf(831,plain,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ B @ A @ ( c_Relation_OId__on @ B @ A ) ),
inference(cnf,[status(esa)],[830]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__commute) ).
thf(1853,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ B ) @ A ) @ C ) @ D ) @ E )
= ( hAPP @ A @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cut__apply) ).
thf(1894,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ B ) @ A ) @ C ) @ D ) @ E )
= ( hAPP @ A @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(291,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/sandbox/benchmark/theBenchmark.p',fact_Range__empty) ).
thf(1524,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)],[291]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
thf(736,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)],[78]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ C ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ 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 ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ ( c_Fun_Ofun__upd @ D @ G @ C @ A @ F ) ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ ( c_Set_Oinsert @ D @ A @ B ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__funcset__fun__upd__extends__rangeI) ).
thf(2097,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ C ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ 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 ) ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ ( c_Fun_Ofun__upd @ D @ G @ C @ A @ F ) ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ ( c_Set_Oinsert @ D @ A @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(396,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
thf(1933,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Product__Type_OSigma @ C @ B @ A @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__empty2) ).
thf(616,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Product__Type_OSigma @ C @ B @ A @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Product__Type_OSigma @ E @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ A ) ) @ ( c_Product__Type_OSigma @ E @ D @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib1) ).
thf(2079,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Product__Type_OSigma @ E @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ A ) ) @ ( c_Product__Type_OSigma @ E @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(496,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).
thf(2361,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb1) ).
thf(2084,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ A ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(2569,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ A ) )
| ( ( hAPP @ ( c_COMBI @ B ) @ A )
!= ( hAPP @ v_F @ v_Q____ ) ) ),
inference(paramod_ordered,[status(thm)],[1116,519]) ).
thf(2595,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ A ) )
| ( ( c_COMBI @ B )
!= v_F )
| ( A != v_Q____ ) ),
inference(simp,[status(thm)],[2569]) ).
thf(2624,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ v_Q____ ) )
| ( ( c_COMBI @ A )
!= v_F ) ),
inference(simp,[status(thm)],[2595]) ).
thf(92,axiom,
class_Orderings_Olinorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(784,plain,
class_Orderings_Olinorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(188,axiom,
! [A: $i] :
( ( hAPP @ v_Q____ @ A )
= ( c_HOL_OLet @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ c_fequal @ v_a____ ) @ v_a_H____ ) ) @ ( hAPP @ v_P____ @ A ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ ( hAPP @ v_P____ @ A ) @ v_a_H____ @ v_a____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ c_fequal @ v_b____ ) @ v_b_H____ ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ c_Arrow__Order__Mirabelle_Oabove ) @ v_b____ ) ) @ v_b_H____ ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Q__def) ).
thf(1117,plain,
! [A: $i] :
( ( hAPP @ v_Q____ @ A )
= ( c_HOL_OLet @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ c_fequal @ v_a____ ) @ v_a_H____ ) ) @ ( hAPP @ v_P____ @ A ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ ( hAPP @ v_P____ @ A ) @ v_a_H____ @ v_a____ ) ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( c_If @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ c_fequal @ v_b____ ) @ v_b_H____ ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ c_Arrow__Order__Mirabelle_Oabove ) @ v_b____ ) ) @ v_b_H____ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(167,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_F ) @ ( c_FuncSet_OPi @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ c_Arrow__Order__Mirabelle_OProf @ ( c_COMBK @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I1_J) ).
thf(1043,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_F ) @ ( c_FuncSet_OPi @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ c_Arrow__Order__Mirabelle_OProf @ ( c_COMBK @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Orefl__on @ C @ B @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Product__Type_OSigma @ C @ C @ B @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C @ B ) ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__def) ).
thf(1801,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Orefl__on @ C @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Product__Type_OSigma @ C @ C @ B @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C @ B ) ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) @ A ) ) ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Product__Type_OSigma @ C @ C @ B @ ( c_COMBK @ ( tc_fun @ C @ tc_HOL_Obool ) @ C @ B ) ) )
& ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) @ A ) ) ) )
=> ( c_Relation_Orefl__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(599,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)],[32]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaE2) ).
thf(1376,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( c_Predicate_ODomainP @ B @ A @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
thf(1877,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( c_Predicate_ODomainP @ B @ A @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib2) ).
thf(816,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI2) ).
thf(895,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_OSigma @ F @ E @ ( c_Set_Oinsert @ F @ D @ C ) @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ ( c_Set_Oinsert @ E @ B @ A ) ) )
= ( c_Set_Oinsert @ ( tc_prod @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ F @ E @ C @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ ( c_Set_Oinsert @ E @ B @ A ) ) ) ) @ ( c_Product__Type_OSigma @ F @ E @ ( c_Set_Oinsert @ F @ D @ C ) @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__times__insert) ).
thf(1149,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_OSigma @ F @ E @ ( c_Set_Oinsert @ F @ D @ C ) @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ ( c_Set_Oinsert @ E @ B @ A ) ) )
= ( c_Set_Oinsert @ ( tc_prod @ F @ E ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ F @ E @ C @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ ( c_Set_Oinsert @ E @ B @ A ) ) ) ) @ ( c_Product__Type_OSigma @ F @ E @ ( c_Set_Oinsert @ F @ D @ C ) @ ( c_COMBK @ ( tc_fun @ E @ tc_HOL_Obool ) @ F @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(1697,plain,
! [B: $i,A: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
inference(cnf,[status(esa)],[1696]) ).
thf(1698,plain,
! [B: $i,A: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
inference(lifteq,[status(thm)],[1697]) ).
thf(1699,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ A ) @ A ) ),
inference(simp,[status(thm)],[1698]) ).
thf(2575,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ C )
| ( A != C )
| ( ( hAPP @ ( c_COMBI @ B ) @ A )
!= ( hAPP @ c_fNot @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1116,2473]) ).
thf(2603,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ B )
| ( ( c_COMBI @ A )
!= c_fNot )
| ( B != B ) ),
inference(simp,[status(thm)],[2575]) ).
thf(2632,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ B )
| ( ( c_COMBI @ A )
!= c_fNot ) ),
inference(simp,[status(thm)],[2603]) ).
thf(2662,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_COMBI @ B )
!= c_fNot )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ A ) @ A ) )
!= ( hBOOL @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1699,2632]) ).
thf(2663,plain,
! [A: $i] :
( ( c_COMBI @ A )
!= c_fNot ),
inference(pattern_uni,[status(thm)],[2662:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( hAPP @ ( hAPP @ c_fequal @ E ) @ E ))]]) ).
thf(2664,plain,
! [A: $i] :
( ( c_COMBI @ A )
!= c_fNot ),
inference(simp,[status(thm)],[2663]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__idem) ).
thf(1820,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(106,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/sandbox/benchmark/theBenchmark.p',fact_bot__least) ).
thf(811,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)],[106]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
thf(2182,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[450]) ).
thf(446,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/sandbox/benchmark/theBenchmark.p',fact_Id__on__empty) ).
thf(2129,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)],[446]) ).
thf(100,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
thf(799,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)],[100]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2D2) ).
thf(1162,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',fact_singleton__inject) ).
thf(848,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)],[114]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',fact_subset__empty) ).
thf(626,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)],[41]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I7_J) ).
thf(915,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ ( c_FuncSet_Ocompose @ F @ D @ E @ C @ B @ A ) ) @ ( c_FuncSet_Oextensional @ F @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compose__extensional) ).
thf(1556,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ ( c_FuncSet_Ocompose @ F @ D @ E @ C @ B @ A ) ) @ ( c_FuncSet_Oextensional @ F @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_insert__is__Un) ).
thf(769,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ A )
= ( hAPP @ ( hAPP @ ( 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)],[86]) ).
thf(2537,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ B ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ A ) @ A ) )
!= ( hBOOL @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1699,2282]) ).
thf(2538,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ c_fNot @ ( hAPP @ ( hAPP @ c_fequal @ A ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[2537:[bind(A,$thf( D )),bind(B,$thf( hAPP @ ( hAPP @ c_fequal @ D ) @ D ))]]) ).
thf(2553,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ c_fNot @ ( hAPP @ ( hAPP @ c_fequal @ A ) @ A ) ) ),
inference(simp,[status(thm)],[2538]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',fact_insert__Diff__single) ).
thf(668,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)],[56]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__iff) ).
thf(1177,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(263,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__iff) ).
thf(1381,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
thf(932,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Ointros) ).
thf(1061,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( 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)],[172]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ C ) @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf2I) ).
thf(1112,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ F ) @ C ) @ E ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__distrib2) ).
thf(1688,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Osingle__valued @ C @ B @ A )
<=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ E ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ F ) ) @ A ) )
=> ( E = F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__def) ).
thf(2350,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Osingle__valued @ C @ B @ A )
=> ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ E ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ F ) ) @ A ) )
=> ( E = F ) ) ) )
& ( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ E ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( 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)],[495]) ).
thf(2568,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ A ) @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( hAPP @ ( c_COMBI @ B ) @ A )
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) ),
inference(paramod_ordered,[status(thm)],[1116,519]) ).
thf(2591,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ A ) @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( c_COMBI @ B )
!= ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) )
| ( A != v_b____ ) ),
inference(simp,[status(thm)],[2568]) ).
thf(2620,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ v_b____ ) @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( c_COMBI @ A )
!= ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) ) ),
inference(simp,[status(thm)],[2591]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le1) ).
thf(883,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ E ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ F ) ) @ A ) )
=> ( E = F ) ) )
=> ( c_Relation_Osingle__valued @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valuedI) ).
thf(2288,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ B ) @ D ) @ E ) ) @ A ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ B ) ) @ ( hAPP @ ( hAPP @ ( 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)],[480]) ).
thf(203,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ v_F @ v_Q____ ) ) @ c_Arrow__Order__Mirabelle_OLin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096F_AQ_A_058_ALin_096) ).
thf(1165,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ v_F @ v_Q____ ) ) @ c_Arrow__Order__Mirabelle_OLin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(2667,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ v_F @ v_Q____ ) ) @ c_Arrow__Order__Mirabelle_OLin ) )
!= ( hBOOL @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1165,2282]) ).
thf(2668,plain,
~ ( hBOOL @ ( hAPP @ c_fNot @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ v_F @ v_Q____ ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(pattern_uni,[status(thm)],[2667:[bind(A,$thf( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( hAPP @ v_F @ v_Q____ ) ) @ c_Arrow__Order__Mirabelle_OLin ))]]) ).
thf(2776,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ ( hAPP @ ( hAPP @ ( 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 ) ) )
| ( ( hAPP @ ( c_COMBI @ B ) @ A )
!= ( hAPP @ v_F @ v_Q____ ) ) ),
inference(paramod_ordered,[status(thm)],[1116,2668]) ).
thf(2787,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ ( hAPP @ ( hAPP @ ( 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_COMBI @ B )
!= v_F )
| ( A != v_Q____ ) ),
inference(simp,[status(thm)],[2776]) ).
thf(2797,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_Q____ ) @ c_Arrow__Order__Mirabelle_OLin ) ) )
| ( ( c_COMBI @ A )
!= v_F ) ),
inference(simp,[status(thm)],[2787]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__apply) ).
thf(2390,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(458,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_emptyE) ).
thf(2207,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(327,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( c_COMBK @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ A ) ) @ c_Arrow__Order__Mirabelle_OProf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).
thf(1694,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ ( c_COMBK @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_Arrow__Order__Mirabelle_Oindi @ A ) ) @ c_Arrow__Order__Mirabelle_OProf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__commute) ).
thf(2069,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(154,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_P____ @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a_H____ ) @ v_b_H____ ) ) @ ( hAPP @ v_P_H____ @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C1_C) ).
thf(983,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_P____ @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a_H____ ) @ v_b_H____ ) ) @ ( hAPP @ v_P_H____ @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a_H____ ) @ v_b_H____ ) ) @ ( hAPP @ v_P_H____ @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) @ v_b____ ) ) @ ( hAPP @ v_P____ @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(509,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ODomain @ E @ D @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ C ) @ B ) @ A ) )
= ( c_Set_Oinsert @ E @ C @ ( c_Relation_ODomain @ E @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__insert) ).
thf(2418,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ODomain @ E @ D @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) @ ( hAPP @ ( hAPP @ ( 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)],[509]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ D @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__downwards__aux) ).
thf(2401,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ D @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_le__supE) ).
thf(2212,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( 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)],[460]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
thf(959,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( c_member @ C ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A @ ( c_Transitive__Closure_Ortranclp @ C @ B ) )
=> ( ( c_Transitive__Closure_Ortranclp @ C @ A )
= ( c_Transitive__Closure_Ortranclp @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclp__subset) ).
thf(695,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A @ ( c_Transitive__Closure_Ortranclp @ C @ B ) )
=> ( ( c_Transitive__Closure_Ortranclp @ C @ A )
= ( c_Transitive__Closure_Ortranclp @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Odistrib__lattice @ B )
=> ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).
thf(636,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Odistrib__lattice @ B )
=> ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb1) ).
thf(1044,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
thf(1413,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Set_Oinsert @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if1) ).
thf(1809,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Set_Oinsert @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( c_Predicate_ORangeP @ B @ A @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
thf(1662,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( c_Predicate_ORangeP @ B @ A @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1I) ).
thf(1304,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ D ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).
thf(1166,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(531,plain,
! [D: $i,C: $i,B: $i,A: $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(cnf,[status(esa)],[530]) ).
thf(323,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffI) ).
thf(1684,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[323]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I1) ).
thf(2124,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ D ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oassoc) ).
thf(1340,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
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/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(553,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(423,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Predicate_ORangeP @ D @ C @ B @ A )
<=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
thf(2054,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Predicate_ORangeP @ D @ C @ B @ A )
=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ A ) ) )
& ( ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ A ) )
=> ( c_Predicate_ORangeP @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( c_FuncSet_Oextensional @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Set_Oinsert @ ( tc_fun @ B @ A ) @ ( c_COMBK @ A @ B @ ( c_HOL_Oundefined @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__empty) ).
thf(722,plain,
! [A: $i,B: $i] :
( ( c_FuncSet_Oextensional @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Set_Oinsert @ ( tc_fun @ B @ A ) @ ( c_COMBK @ A @ B @ ( c_HOL_Oundefined @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ A ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb2) ).
thf(1203,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_OaccI) ).
thf(1208,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Osemilattice__sup @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).
thf(589,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)],[28]) ).
thf(794,plain,
v_a_H____ != v_b_H____,
inference(polarity_switch,[status(thm)],[793]) ).
thf(795,plain,
v_b_H____ != v_a_H____,
inference(lifteq,[status(thm)],[794]) ).
thf(488,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__right) ).
thf(2318,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__crazy) ).
thf(663,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower1) ).
thf(548,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
thf(1134,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
thf(648,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)],[48]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb2) ).
thf(2333,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ C ) @ B ) @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distrib__inf__le) ).
thf(1145,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__fun__def) ).
thf(1018,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ E ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ E ) @ ( hAPP @ C @ A ) ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__Sigma__iff) ).
thf(2256,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ C ) @ ( hAPP @ A @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ A ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
thf(1748,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ A ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
thf(1003,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ D @ ( c_COMBC @ C @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_prod @ D @ C ) ) @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ D @ ( c_COMBB @ ( tc_prod @ D @ C ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ C @ ( c_member @ ( tc_prod @ D @ C ) ) ) ) @ ( c_Product__Type_OPair @ D @ C ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Product__Type_OSigma @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ B ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib2) ).
thf(1516,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Product__Type_OSigma @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_COMBS @ E @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) @ B ) ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ B ) ) @ ( c_Product__Type_OSigma @ E @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(401,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/sandbox/benchmark/theBenchmark.p',fact_Sigma__empty1) ).
thf(1961,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)],[401]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( 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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__greatest) ).
thf(1025,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( 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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Relation_OId__on @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
thf(1070,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Relation_OId__on @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards) ).
thf(887,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Wellfounded_Oacc @ D @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(2012,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(228,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb) ).
thf(1252,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(2699,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ v_b____ ) @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( c_COMBI @ C )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( ( hAPP @ ( c_COMBI @ B ) @ A )
!= ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) ) ),
inference(paramod_ordered,[status(thm)],[1116,2619]) ).
thf(2712,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ v_b____ ) @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( c_COMBI @ C )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( ( c_COMBI @ B )
!= ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A != v_a____ ) ),
inference(simp,[status(thm)],[2699]) ).
thf(2720,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( c_COMBI @ B )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( ( c_COMBI @ A )
!= ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(simp,[status(thm)],[2712]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__assoc) ).
thf(1098,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(482,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1CI) ).
thf(2298,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ B ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
thf(580,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(116,axiom,
class_Lattices_Olattice @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
thf(855,plain,
class_Lattices_Olattice @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_singleton__iff) ).
thf(1230,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[223]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD) ).
thf(1484,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ E ) ) @ A ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ E ) @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( c_HOL_Oundefined @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__def) ).
thf(1987,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( hAPP @ A @ D ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( c_FuncSet_Orestrict @ E @ B @ A @ C ) @ D )
= ( c_HOL_Oundefined @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_Oextensional__funcset @ F @ E @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__funcset__mem) ).
thf(1317,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ E ) ) @ D ) @ ( c_FuncSet_Oextensional__funcset @ F @ E @ C @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
thf(951,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) )
& ( ( hBOOL @ ( hAPP @ A @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD1) ).
thf(1579,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ B ) @ A ) ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__distrib1) ).
thf(1285,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equals0D) ).
thf(1220,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_sup1E) ).
thf(907,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[132]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_Un__empty__right) ).
thf(673,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( 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)],[58]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
<=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__inf) ).
thf(2092,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C ) @ B ) @ A )
= B ) )
& ( ( ( hAPP @ ( hAPP @ ( 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)],[437]) ).
thf(178,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__least) ).
thf(1085,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(576,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb1) ).
thf(744,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(350,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ ( c_FuncSet_OPi @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ c_Arrow__Order__Mirabelle_OProf @ ( c_COMBK @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [D: $i,E: $i] :
( ( D != E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ C ) ) ) ) ) )
=> ( c_Arrow__Order__Mirabelle_Odictator @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictatorI) ).
thf(1766,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ ( c_FuncSet_OPi @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ c_Arrow__Order__Mirabelle_OProf @ ( c_COMBK @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) )
=> ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [D: $i,E: $i] :
( ( D != E )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D ) @ E ) ) @ ( hAPP @ B @ C ) ) ) ) ) )
=> ( c_Arrow__Order__Mirabelle_Odictator @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(407,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__idem) ).
thf(1981,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(330,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ B ) )
= ( c_Orderings_Obot__class_Obot @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__bot__right) ).
thf(1702,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ B ) )
= ( c_Orderings_Obot__class_Obot @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(476,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 @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
thf(2279,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 @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( ( c_Product__Type_OSigma @ C @ F @ B @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C @ D ) )
= ( c_Product__Type_OSigma @ C @ F @ A @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C @ D ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__eq__cancel2) ).
thf(1052,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( ( ( c_Product__Type_OSigma @ C @ F @ B @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C @ D ) )
= ( c_Product__Type_OSigma @ C @ F @ A @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C @ D ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Product__Type_OSigma @ C @ F @ B @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C @ D ) )
= ( c_Product__Type_OSigma @ C @ F @ A @ ( c_COMBK @ ( tc_fun @ F @ tc_HOL_Obool ) @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(319,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Int) ).
thf(1670,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__subset) ).
thf(1717,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( 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)],[336]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ORange @ B @ D @ A ) ) )
<=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ D ) @ E ) @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__iff) ).
thf(1881,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ORange @ B @ D @ A ) ) )
=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ D ) @ E ) @ C ) ) @ A ) ) )
& ( ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ D ) @ E ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ORange @ B @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(859,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ F ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ D @ A ) @ E ) @ F ) @ B ) @ C )
= ( hAPP @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tfl__cut__apply) ).
thf(991,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) ) @ F ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ D @ A ) @ E ) @ F ) @ B ) @ C )
= ( hAPP @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(384,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_mktop__Lin) ).
thf(1898,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[384]) ).
thf(367,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 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryE) ).
thf(1849,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 @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(270,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI1) ).
thf(1421,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(137,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d1_I1_J) ).
thf(929,plain,
v_a____ != v_b____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(930,plain,
v_a____ != v_b____,
inference(polarity_switch,[status(thm)],[929]) ).
thf(931,plain,
v_b____ != v_a____,
inference(lifteq,[status(thm)],[930]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ C @ B ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclp_Ortrancl__refl) ).
thf(1949,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ C @ B ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__def) ).
thf(1654,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Set_Oinsert @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right) ).
thf(2215,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Set_Oinsert @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int) ).
thf(759,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
thf(1120,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)],[189]) ).
thf(1121,plain,
( ! [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ D @ C @ B ) @ A ) )
=> ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) )
=> ! [D: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ D @ C @ B ) @ A ) ) ) ),
inference(miniscope,[status(thm)],[1120]) ).
thf(1122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C != A )
| ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ D @ C @ B ) @ A ) ) ),
inference(cnf,[status(esa)],[1121]) ).
thf(1125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C != A )
| ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ D @ C @ B ) @ A ) ) ),
inference(lifteq,[status(thm)],[1122]) ).
thf(1126,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ B ) @ A ) ),
inference(simp,[status(thm)],[1125]) ).
thf(210,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/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
thf(1189,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)],[210]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
thf(1010,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F = E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= A ) )
& ( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(2906,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_P_H____ ) @ c_Arrow__Order__Mirabelle_OProf ) )
!= ( hBOOL @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1886,2282]) ).
thf(2907,plain,
~ ( hBOOL @ ( hAPP @ c_fNot @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_P_H____ ) @ c_Arrow__Order__Mirabelle_OProf ) ) ),
inference(pattern_uni,[status(thm)],[2906:[bind(A,$thf( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_P_H____ ) @ c_Arrow__Order__Mirabelle_OProf ))]]) ).
thf(184,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ B ) ) @ ( c_COMBI @ B ) ) @ ( c_FuncSet_OPi @ B @ B @ A @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__id) ).
thf(1108,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ B @ B ) ) @ ( c_COMBI @ B ) ) @ ( c_FuncSet_OPi @ B @ B @ A @ ( c_COMBK @ ( tc_fun @ B @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(2572,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ A @ v_b____ ) ) @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( hAPP @ ( c_COMBI @ B ) @ A )
!= ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_a____ ) ) ),
inference(paramod_ordered,[status(thm)],[1116,519]) ).
thf(2597,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ A @ v_b____ ) ) @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( c_COMBI @ B )
!= ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A != v_a____ ) ),
inference(simp,[status(thm)],[2572]) ).
thf(2626,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ v_a____ @ v_b____ ) ) @ ( hAPP @ v_F @ v_Q____ ) ) )
| ( ( c_COMBI @ A )
!= ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(simp,[status(thm)],[2597]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ E @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ E @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ E @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclp__trans) ).
thf(1918,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ E @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ E @ D ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ E @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_OPi @ E @ D @ B @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( c_FuncSet_Ocompose @ E @ D @ D @ B @ ( c_FuncSet_Orestrict @ D @ D @ ( c_COMBI @ D ) @ A ) @ C )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__compose) ).
thf(1649,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_OPi @ E @ D @ B @ ( c_COMBK @ ( tc_fun @ D @ tc_HOL_Obool ) @ E @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ D ) ) @ C ) @ ( c_FuncSet_Oextensional @ E @ D @ B ) ) )
=> ( ( c_FuncSet_Ocompose @ E @ D @ D @ B @ ( c_FuncSet_Orestrict @ D @ D @ ( c_COMBI @ D ) @ A ) @ C )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
thf(671,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)],[57]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffE) ).
thf(1817,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
thf(1157,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ B ) @ A ) @ C ) @ D ) @ E )
= ( hAPP @ A @ E ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ B ) @ A ) @ C ) @ D ) @ E )
= ( c_HOL_Oundefined @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cut__def) ).
thf(1321,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ B ) @ A ) @ C ) @ D ) @ E )
= ( hAPP @ A @ E ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ B ) @ A ) @ C ) @ D ) @ E )
= ( c_HOL_Oundefined @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oassoc) ).
thf(1834,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Orefl__on @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD) ).
thf(1913,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Orefl__on @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ A ) @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D1) ).
thf(2310,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( c_Set_Oinsert @ C @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(1844,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( c_Set_Oinsert @ C @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(2167,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(470,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ ( c_Relation_Oinv__image @ C @ F @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ ( hAPP @ A @ E ) ) @ ( hAPP @ A @ D ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__inv__image) ).
thf(2251,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ ( c_Relation_Oinv__image @ C @ F @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ ( hAPP @ A @ E ) ) @ ( hAPP @ A @ D ) ) ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ ( hAPP @ A @ E ) ) @ ( hAPP @ A @ D ) ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ E ) @ D ) ) @ ( c_Relation_Oinv__image @ C @ F @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Oequations) ).
thf(1903,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Relation_OId__on @ C @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__onE) ).
thf(1508,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ B ) @ ( c_Relation_OId__on @ C @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( B
!= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI1) ).
thf(1101,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__iff) ).
thf(2026,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Wellfounded_Oaccp @ C @ A ) @ ( c_Wellfounded_Oaccp @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp__subset) ).
thf(786,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Wellfounded_Oaccp @ C @ A ) @ ( c_Wellfounded_Oaccp @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__right) ).
thf(781,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Transitive__Closure_Ortranclp @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( c_Transitive__Closure_Ortranclp @ C @ B ) ) @ ( c_Transitive__Closure_Ortranclp @ C @ A ) ) )
= ( c_Transitive__Closure_Ortranclp @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclp__sup__rtranclp) ).
thf(1276,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Transitive__Closure_Ortranclp @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ ( c_Transitive__Closure_Ortranclp @ C @ B ) ) @ ( c_Transitive__Closure_Ortranclp @ C @ A ) ) )
= ( c_Transitive__Closure_Ortranclp @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnE) ).
thf(1590,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(813,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)],[107]) ).
thf(338,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_ORange @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_Range__Un__eq) ).
thf(1721,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_ORange @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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)],[338]) ).
thf(449,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ A ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ E ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ B @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ v_F @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ v_F @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_AP_058Prof_O_AALL_AP_H_058Prof_O_AALL_Aa_Ab_O_A_IALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_J_J_A_N_N_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_J_096) ).
thf(2174,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ A ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i,D: $i] :
( ! [E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ B @ E ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ E ) ) ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ v_F @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ v_F @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ v_F @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ v_F @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(478,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/sandbox/benchmark/theBenchmark.p',fact_acc__subset) ).
thf(2283,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)],[478]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
thf(1558,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ F @ E @ D ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).
thf(2262,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_FuncSet_Oextensional__funcset @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A )
= ( c_Set_Oinsert @ ( tc_fun @ C @ B ) @ ( c_COMBK @ B @ C @ ( c_HOL_Oundefined @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ B ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__funcset__empty__domain) ).
thf(568,plain,
! [A: $i,B: $i,C: $i] :
( ( c_FuncSet_Oextensional__funcset @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A )
= ( c_Set_Oinsert @ ( tc_fun @ C @ B ) @ ( c_COMBK @ B @ C @ ( c_HOL_Oundefined @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ B ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(427,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__other) ).
thf(2066,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( hAPP @ ( c_Fun_Ofun__upd @ D @ C @ B @ E @ A ) @ F )
= ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) @ B ),
inference(cnf,[status(esa)],[548]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Relation_Osingle__valued @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ C ) @ B ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ C ) @ A ) ) @ D ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valuedD) ).
thf(1994,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Relation_Osingle__valued @ F @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ C ) @ B ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ C ) @ A ) ) @ D ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(113,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/sandbox/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
thf(832,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)],[113]) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',fact_Diff__insert2) ).
thf(684,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)],[62]) ).
thf(463,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_P____ ) @ c_Arrow__Order__Mirabelle_OProf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096P_A_058_AProf_096) ).
thf(2230,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_P____ ) @ c_Arrow__Order__Mirabelle_OProf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(418,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb) ).
thf(2036,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__acc__down) ).
thf(1309,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ~ ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ C ) @ F ) @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup2CI) ).
thf(2421,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) @ C ) @ F ) @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(800,plain,
! [B: $i,A: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A ),
inference(cnf,[status(esa)],[799]) ).
thf(254,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/sandbox/benchmark/theBenchmark.p',fact_bot__apply) ).
thf(1348,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)],[254]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ E ) @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ E ) @ A ) @ C ) @ B ) )
<=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ G ) @ B ) ) @ C ) )
=> ( ( hAPP @ D @ G )
= ( hAPP @ A @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cuts__eq) ).
thf(2102,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ E ) @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ E ) @ A ) @ C ) @ B ) )
=> ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ G ) @ B ) ) @ C ) )
=> ( ( hAPP @ D @ G )
= ( hAPP @ A @ G ) ) ) )
& ( ! [G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ F ) @ G ) @ B ) ) @ C ) )
=> ( ( hAPP @ D @ G )
= ( hAPP @ A @ G ) ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ E ) @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Recdef_Ocut @ F @ E ) @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntI) ).
thf(1512,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ C @ B ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclp_Oequations_I1_J) ).
thf(1546,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ C @ B ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ C ) ) @ B ) @ ( c_FuncSet_Oextensional__funcset @ F @ C @ ( c_Set_Oinsert @ F @ E @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ C ) ) @ ( c_Fun_Ofun__upd @ F @ C @ B @ E @ ( c_HOL_Oundefined @ C ) ) ) @ ( c_FuncSet_Oextensional__funcset @ F @ C @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__funcset__restrict__domain) ).
thf(1527,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ C ) ) @ B ) @ ( c_FuncSet_Oextensional__funcset @ F @ C @ ( c_Set_Oinsert @ F @ E @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ F @ C ) ) @ ( c_Fun_Ofun__upd @ F @ C @ B @ E @ ( c_HOL_Oundefined @ C ) ) ) @ ( c_FuncSet_Oextensional__funcset @ F @ C @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Un) ).
thf(790,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
thf(865,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ C ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ E @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ E @ E ) @ D ) @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ B @ A ) ) )
=> ( ( C != B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
thf(867,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Set_Oinsert @ D @ B @ A ) ) )
=> ( ( C != B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(349,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(1757,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(104,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
thf(807,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)],[104]) ).
thf(300,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__sup @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ B ) @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__idem) ).
thf(1561,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__sup @ B )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ B ) @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ H ) @ F ) @ D ) ) @ B ) )
| ( ( F = D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ E ) @ C ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
thf(897,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ H ) @ F ) @ D ) ) @ B ) )
| ( ( F = D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ E ) @ C ) ) @ A ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ H @ H ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ H ) @ F ) @ D ) ) @ B ) )
| ( ( F = D )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ G @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ G @ G ) @ E ) @ C ) ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ H @ G ) @ D ) @ C ) ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(498,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/sandbox/benchmark/theBenchmark.p',fact_acyclic__subset) ).
thf(2366,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)],[498]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Ointernal__split @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_internal__split__conv) ).
thf(2063,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Ointernal__split @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(98,axiom,
class_Lattices_Odistrib__lattice @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
thf(796,plain,
class_Lattices_Odistrib__lattice @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq2) ).
thf(1436,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) ) @ D ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ F @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ F @ ( c_COMBC @ E @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ ( tc_prod @ F @ E ) ) @ ( tc_fun @ E @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) @ F @ ( c_COMBB @ ( tc_prod @ F @ E ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ tc_HOL_Obool ) @ E @ ( c_member @ ( tc_prod @ F @ E ) ) ) ) @ ( c_Product__Type_OPair @ F @ E ) ) ) ) @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(372,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 )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
thf(1859,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 )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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)],[372]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_Osimps) ).
thf(918,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ C @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ C @ C ) @ D ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper2) ).
thf(801,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(258,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
thf(1363,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( 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] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D @ C @ A ) ) @ B )
= ( c_Set_Oinsert @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if1) ).
thf(1314,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( c_Set_Oinsert @ D @ C @ A ) ) @ B )
= ( c_Set_Oinsert @ D @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(1288,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ C ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ ( c_Fun_Ofun__upd @ D @ G @ C @ A @ F ) ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ ( c_Set_Oinsert @ D @ A @ B ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensional__funcset__extend__domainI) ).
thf(1710,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ C ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ D @ G ) ) @ ( c_Fun_Ofun__upd @ D @ G @ C @ A @ F ) ) @ ( c_FuncSet_Oextensional__funcset @ D @ G @ ( c_Set_Oinsert @ D @ A @ B ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( class_Orderings_Obot @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
thf(720,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( class_Orderings_Obot @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(395,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnCI) ).
thf(1930,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',fact_subset__singletonD) ).
thf(740,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)],[79]) ).
thf(466,axiom,
c_Arrow__Order__Mirabelle_Ounanimity @ v_F,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u) ).
thf(2241,plain,
c_Arrow__Order__Mirabelle_Ounanimity @ v_F,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__I_H) ).
thf(1129,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ F ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ F ) ) @ ( hAPP @ A @ F ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ E @ C ) ) @ B ) @ ( c_FuncSet_OPi @ E @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SigmaD1) ).
thf(2430,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ F @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C ) ) @ ( c_Product__Type_OSigma @ F @ E @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__assoc) ).
thf(1152,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib) ).
thf(596,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(473,axiom,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_Odictator @ B @ A )
<=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hAPP @ B @ C )
= ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictator__def) ).
thf(2265,plain,
! [A: $i,B: $i] :
( ( ( c_Arrow__Order__Mirabelle_Odictator @ B @ A )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hAPP @ B @ C )
= ( hAPP @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ C ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ( ( hAPP @ B @ C )
= ( hAPP @ C @ A ) ) )
=> ( c_Arrow__Order__Mirabelle_Odictator @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(7,axiom,
class_Lattices_Osemilattice__sup @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
thf(528,plain,
class_Lattices_Osemilattice__sup @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ODomain @ D @ B @ A ) ) )
<=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ C ) @ E ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__iff) ).
thf(1500,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ODomain @ D @ B @ A ) ) )
=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ C ) @ E ) ) @ A ) ) )
& ( ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ C ) @ E ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ODomain @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
thf(822,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)],[110]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
thf(1925,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(1901,plain,
v_b____ != v_a_H____,
inference(polarity_switch,[status(thm)],[1900]) ).
thf(1902,plain,
v_a_H____ != v_b____,
inference(lifteq,[status(thm)],[1901]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if0) ).
thf(1505,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
<=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Un__eq) ).
thf(607,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= A ) )
& ( ( ( hAPP @ ( hAPP @ ( 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)],[35]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_FuncSet_Ocompose @ F @ E @ D @ C @ B @ A )
= ( c_FuncSet_Orestrict @ F @ D @ ( hAPP @ ( c_COMBB @ E @ D @ F @ B ) @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compose__def) ).
thf(1384,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_FuncSet_Ocompose @ F @ E @ D @ C @ B @ A )
= ( c_FuncSet_Orestrict @ F @ D @ ( hAPP @ ( c_COMBB @ E @ D @ F @ B ) @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(295,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ A )
<=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unanimity__def) ).
thf(1537,plain,
! [A: $i] :
( ( ( c_Arrow__Order__Mirabelle_Ounanimity @ A )
=> ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ B ) ) ) ) ) )
& ( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ B ) @ c_Arrow__Order__Mirabelle_OProf ) )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ B @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C ) @ D ) ) @ ( hAPP @ A @ B ) ) ) ) )
=> ( c_Arrow__Order__Mirabelle_Ounanimity @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(102,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 @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greatest) ).
thf(803,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 @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(2997,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_P____ ) @ c_Arrow__Order__Mirabelle_OProf ) )
!= ( hBOOL @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2230,2282]) ).
thf(2998,plain,
~ ( hBOOL @ ( hAPP @ c_fNot @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_P____ ) @ c_Arrow__Order__Mirabelle_OProf ) ) ),
inference(pattern_uni,[status(thm)],[2997:[bind(A,$thf( hAPP @ ( hAPP @ ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) @ v_P____ ) @ c_Arrow__Order__Mirabelle_OProf ))]]) ).
thf(538,plain,
! [C: $i,B: $i,A: $i] :
( ( C != B )
| ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B ) ),
inference(cnf,[status(esa)],[536]) ).
thf(542,plain,
! [C: $i,B: $i,A: $i] :
( ( C != B )
| ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B ) ),
inference(lifteq,[status(thm)],[538]) ).
thf(543,plain,
! [B: $i,A: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ B ),
inference(simp,[status(thm)],[542]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI2) ).
thf(2059,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D ) @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb1) ).
thf(676,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(435,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ODomain @ D @ B @ A ) ) )
=> ~ ! [E: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ C ) @ E ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainE) ).
thf(2087,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_Relation_ODomain @ D @ B @ A ) ) )
=> ~ ! [E: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ B ) @ C ) @ E ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
thf(708,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)],[68]) ).
thf(1866,plain,
( ! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) )
=> ( B = A ) )
& ! [A: $i,B: $i] :
( ( B = A )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) ) ) ),
inference(miniscope,[status(thm)],[1865]) ).
thf(1867,plain,
! [C: $i,B: $i,A: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) ) ),
inference(cnf,[status(esa)],[1866]) ).
thf(1869,plain,
! [C: $i,B: $i,A: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) ) ),
inference(lifteq,[status(thm)],[1867]) ).
thf(1870,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ ( hAPP @ c_fequal @ A ) ) ),
inference(simp,[status(thm)],[1869]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Recdef_Oadm__wf @ D @ C @ B @ A )
<=> ! [E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ H ) @ G ) ) @ B ) )
=> ( ( hAPP @ E @ H )
= ( hAPP @ F @ H ) ) )
=> ( ( hAPP @ ( hAPP @ A @ E ) @ G )
= ( hAPP @ ( hAPP @ A @ F ) @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_adm__wf__def) ).
thf(2321,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Recdef_Oadm__wf @ D @ C @ B @ A )
=> ! [E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ H ) @ G ) ) @ B ) )
=> ( ( hAPP @ E @ H )
= ( hAPP @ F @ H ) ) )
=> ( ( hAPP @ ( hAPP @ A @ E ) @ G )
= ( hAPP @ ( hAPP @ A @ F ) @ G ) ) ) )
& ( ! [E: $i,F: $i,G: $i] :
( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ D @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ H ) @ G ) ) @ B ) )
=> ( ( hAPP @ E @ H )
= ( hAPP @ F @ H ) ) )
=> ( ( hAPP @ ( hAPP @ A @ E ) @ G )
= ( hAPP @ ( hAPP @ A @ F ) @ G ) ) )
=> ( c_Recdef_Oadm__wf @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(1653,plain,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
inference(cnf,[status(esa)],[1652]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD2) ).
thf(940,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_Un__Diff) ).
thf(1184,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) ) @ C ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( 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)],[208]) ).
thf(430,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 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
thf(2074,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 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ B ) @ D ) @ C ) ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(453,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI2) ).
thf(2191,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 @ ( hAPP @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Oabove @ C ) @ E ) @ D ) ) )
<=> ( ( B != A )
& ( ( B = D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ E ) @ A ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ E ) ) @ C ) ) ) )
& ( ( A != D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__above) ).
thf(1449,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( 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 ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Oabove @ C ) @ E ) @ D ) ) )
=> ( ( B != A )
& ( ( B = D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ E ) @ A ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ E ) ) @ C ) ) ) )
& ( ( A != D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) ) )
& ( ( ( B != A )
& ( ( B = D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ E ) @ A ) ) @ C ) ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ E ) ) @ C ) ) ) )
& ( ( A != D )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ C ) ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Oabove @ C ) @ E ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_OField @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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/sandbox/benchmark/theBenchmark.p',fact_Field__insert) ).
thf(1812,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_OField @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ D @ D ) @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( 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)],[356]) ).
thf(80422,plain,
$false,
inference(cvc4,[status(thm)],[2199,1036,1879,1411,1823,2341,2336,2072,1237,2463,1840,2427,666,1110,1686,645,892,777,555,2363,1750,1211,2210,683,730,2231,2808,994,2248,873,1269,878,614,523,582,762,2099,2282,1608,550,1735,1872,698,747,945,1954,2042,1497,1705,1999,797,2316,1196,1746,2046,2432,1441,1613,1935,2082,1724,565,1887,651,2348,2723,973,885,1529,1967,2039,719,785,2444,619,2274,1279,934,2126,1132,949,2185,1577,1922,638,1379,1147,969,2635,1847,2403,1087,1514,1247,2049,1319,870,2301,1815,2222,1489,1664,1714,1373,1136,2122,1978,937,1283,2090,591,1418,2236,623,1677,2034,1581,966,2281,692,1886,1796,1351,660,1201,1242,527,1696,1169,687,2437,1928,1447,956,2424,774,2371,2242,1345,988,1975,1564,1074,1206,942,2204,2473,925,1306,810,534,714,2061,529,1691,546,793,1915,1708,1047,1730,1021,1519,1255,862,1217,1487,2032,2396,2015,1387,1900,910,825,1343,1355,2277,1570,1174,788,1370,2132,729,1423,2464,1837,1920,852,1951,889,1159,2345,682,2313,1281,522,830,1079,1027,2112,710,1740,1910,1534,1328,1064,1425,593,1360,2245,519,1592,578,1143,2115,1851,1772,1970,1227,1856,725,980,1587,1096,1672,2724,1719,1567,1082,1964,642,1584,1700,1214,1889,2196,526,1842,2472,679,1155,547,622,1249,2304,654,1192,1799,1984,1002,1874,1429,2482,779,605,1627,2285,1114,647,1263,997,1266,2387,1333,633,805,541,657,1712,2076,2368,558,530,586,1434,1857,1187,2440,662,718,1103,1548,856,1301,573,689,2376,733,601,750,1727,819,975,1389,1652,743,2398,2188,772,2393,1752,1428,2193,572,2293,1312,1865,1733,1058,1997,2442,1258,947,1224,1675,1897,2557,2721,831,1853,1894,1524,736,2097,1933,616,2079,2361,2084,2624,784,1117,1043,1801,599,1376,1877,816,895,1149,2664,1820,811,2182,2129,535,799,1162,848,520,626,915,1556,769,2553,668,1177,1381,932,1061,1112,1688,521,2350,2620,883,2288,2797,1000,2390,2207,1694,2069,983,2418,2401,1699,2212,959,695,636,1044,1413,1809,1662,1304,1166,531,1684,2124,2449,1340,553,2054,722,1203,1208,589,795,2318,663,548,1134,648,2333,1145,1018,2256,1748,1003,1516,1961,1025,1070,887,2012,1252,2720,1098,2298,525,580,855,1230,1484,1987,1317,951,1579,1285,1220,907,673,2092,1085,576,744,1766,1981,1702,2279,1052,1670,1717,571,1881,859,991,1898,1849,1421,931,1949,1654,2215,759,1126,1189,1010,2907,1108,2626,1918,1649,671,1817,1157,1321,1834,1913,2310,1844,2167,2251,1903,1508,1101,2026,786,781,1276,1590,813,1721,2174,2283,1558,2262,568,929,2066,549,1994,832,684,2230,2036,1309,2421,800,1116,1348,2102,1512,1546,1527,790,865,867,1757,807,1561,897,2366,2063,796,1436,1859,918,801,1363,1314,1288,1710,2619,532,720,2668,1165,1930,740,2241,1129,2430,1152,596,2265,528,1500,822,1925,1902,1505,1120,607,1384,1537,803,2998,543,2059,676,2087,708,1870,2321,1653,940,1184,2074,2191,1449,1812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SCT128+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 15:37:10 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.93/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.75/1.10 % [INFO] Parsing done (253ms).
% 1.75/1.11 % [INFO] Running in sequential loop mode.
% 2.31/1.31 % [INFO] eprover registered as external prover.
% 2.31/1.32 % [INFO] cvc4 registered as external prover.
% 2.31/1.32 % [INFO] Scanning for conjecture ...
% 2.97/1.45 % [INFO] Found a conjecture and 532 axioms. Running axiom selection ...
% 3.48/1.59 % [INFO] Axiom selection finished. Selected 516 axioms (removed 16 axioms).
% 4.47/1.92 % [INFO] Problem is first-order (TPTP FOF).
% 4.74/1.96 % [INFO] Type checking passed.
% 4.74/1.96 % [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 ...
% 178.58/40.75 % External prover 'cvc4' found a proof!
% 178.58/40.75 % [INFO] Killing All external provers ...
% 178.58/40.75 % Time passed: 40229ms (effective reasoning time: 39636ms)
% 178.58/40.75 % 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)>
% 178.58/40.76 % Axioms used in derivation (516): fact_Int__insert__left__if1, fact_Un__absorb1, fact_wfrec__rel_Ointros, fact_single__valued__Id__on, fact_insertCI, fact_Sigma__Un__distrib1, fact_Field__empty, fact_adm__wf__def, fact_Pi__I, fact_converse__rtrancl__induct2, fact_singleton__iff, fact_refl__onD2, fact_Int__lower1, fact_cut__apply, fact_le__inf__iff, fact_sup1I1, fact_accp_Oequations, fact_inf2I, fact_insert__iff, fact__C1_C, arity_Nat__Onat__Lattices_Olattice, fact_Pi__mono, fact_IIA__def, fact_UnI1, fact_insert__subset, fact_cut__def, fact_unanimity__def, fact_restrictI, fact_compose__Id, fact_Range__Int__subset, fact_inf__sup__aci_I4_J, fact_inf_Oassoc, fact_rtranclD, fact_bot__apply, fact_curry__def, fact_sup__apply, fact_Un__mono, fact_Transitive__Closure_Otrancl__into__trancl, fact_prod_Orecs, fact_extensional__empty, fact_mono__Field, fact_curry__conv, fact_insertI1, fact_Un__empty__left, fact_sup2I2, fact_Un__insert__left, fact_Pi__I_H, fact_Id__compose, fact_in__mktop, fact_inf__absorb1, fact_Pi__anti__mono, fact_extensionalityI, fact_in__mkbot, fact_sup__assoc, fact_curryE, fact_assms_I1_J, fact_SigmaE2, arity_fun__Lattices_Olattice, fact_rtrancl_Ortrancl__refl, fact_acc_Osimps, arity_Nat__Onat__Lattices_Osemilattice__inf, fact_sup__inf__absorb, fact_Int__left__commute, fact_empty__not__insert, fact_d1_I1_J, fact_r__into__trancl_H, fact_tranclD2, fact_inf__sup__distrib2, fact_pred__equals__eq2, fact_rtranclp_Oequations_I1_J, help_c__COMBC__1, fact_inf__sup__ord_I2_J, help_c__fequal__2, fact_below__Lin, fact_converse__rtrancl__induct, fact_rtrancl__mono, fact_rtrancl__subset__rtrancl, fact_insert__not__empty, fact_converse__rtranclE2, fact_bot__fun__def, fact_split__paired__All, fact_Un__Diff__Int, fact_complete__Lin, fact_Range__empty, fact_inf1D2, fact_sup__absorb1, fact_inf__fun__def, fact_equalityD2, fact_inf_Oleft__commute, fact_Int__insert__right, fact_Sigma__empty1, fact_sup__fun__def, fact_extensional__funcset__def, fact_Field__Un, fact_sup__Un__eq2, fact_acc_OaccI, fact_le__supI, fact_le__supI2, fact_predicate2D, fact_bot__empty__eq, fact_Int__empty__left, fact_sup__ge2, fact_Pi__mem, fact_inf2D1, fact_singleton__inject, fact_le__funD, fact_emptyE, fact_le__fun__def, fact_acc__subset, fact_extensional__funcset__mem, fact_rtranclp__reflcl, help_c__COMBS__1, help_c__COMBI__1, fact_fun__upd__same, fact_inf__Int__eq, fact_Domain__empty__iff, fact_extensional__funcset__arb, fact_rtranclp__trans, fact_in__mono, fact_Int__absorb2, fact_Diff__subset__conv, fact_DiffE, arity_fun__Lattices_Osemilattice__inf, fact_Domain__Un__eq, fact_extensional__funcset__fun__upd__extends__rangeI, fact_sup__least, fact_mkbot__Lin, fact_Int__assoc, arity_HOL__Obool__Lattices_Olattice, fact_Int__Un__distrib, fact_funcset__mem, fact_d2_I2_J, fact_rtrancl__subset, fact_subset__singletonD, fact_sup__eq__bot__iff, fact_single__valued__subset, fact_insert__is__Un, fact_Id__on__iff, fact_Diff__insert, fact__096Q_A_058_AProf_096, fact_rtrancl__Un__separator__converseE, fact_inf__commute, fact_fun__upd__idem, fact_tfl__cut__apply, fact_accp__downwards, fact_Int__insert__left, fact_Domain__insert, fact_refl__onD, fact_sup__bot__left, fact_extensional__funcset__empty__domain, arity_fun__Lattices_Osemilattice__sup, fact_acc__downwards, arity_Nat__Onat__Lattices_Odistrib__lattice, fact_distrib__inf__le, fact_dictator__def, fact_sup1I2, fact_inf1I, fact_Domain__mono, fact_insert__code, help_c__fNot__1, arity_HOL__Obool__Lattices_Osemilattice__sup, fact__096F_AQ_A_058_ALin_096, fact_Int__insert__right__if0, fact_Un__left__commute, fact_Un__empty, fact_inf_Oidem, fact_Domain__empty, fact_inf2E, fact_adm__lemma, fact_sup2I1, fact_bot__least, fact_insert__Diff__single, fact_le__infI2, fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_J_096, fact_refl__on__empty, fact_fun__upd__other, fact_d2_I1_J, fact_rtrancl__Un__separatorE, fact_rtrancl__Un__rtrancl, fact_RangeI, fact_extensional__funcset__extend__domainI, fact_compose__extensional, fact_predicate1D, fact_DomainI, fact_inf__sup__ord_I1_J, fact_inf1E, fact_Pi__cong, fact_ex__in__conv, fact_eq__mem, fact_sup__left__commute, fact_subset__insertI, fact_notin__Lin__iff, fact_inf__left__commute, fact_Un__Int__crazy, arity_Nat__Onat__Lattices_Osemilattice__sup, fact_inf__left__idem, fact_accp__subset, fact_Times__Int__distrib1, arity_HOL__Obool__Orderings_Oord, fact_Diff__partition, fact_Id__onE, fact_sup__left__idem, fact_insert__absorb2, fact_le__supI1, fact_insertI2, fact_Times__subset__cancel2, fact_compose__assoc, fact_equals0D, fact_insert__absorb, fact_RangeE, fact_Q__def, fact_fun__upd__apply, fact_converse__rtranclE, fact_inf__bot__right, fact_subset__insert, fact__096P_H_A_058_AProf_096, fact_rtranclp_Ortrancl__into__rtrancl, fact_same__fstI, fact_in__rtrancl__UnI, fact_Un__Int__distrib2, fact_le__funE, fact_extensional__arb, fact_eqset__imp__iff, fact_trancl__empty, fact_trancl__trans, fact_Int__Un__distrib2, fact_Id__on__subset__Times, fact_equalityD1, fact_converse__rtrancl__into__rtrancl, fact_Un__insert__right, fact_trancl__subset__Sigma, fact_inf2D2, arity_Nat__Onat__Orderings_Oord, fact_rtrancl__trans, fact_less__by__empty, fact_extensional__funcset__restrict__domain, fact_extensional__restrict, help_c__fequal__1, fact_in__above, fact_refl__on__Un, fact_insert__inter__insert, fact_irrefl__def, fact_UnI2, fact_insert__commute, fact_fun__upd__triv, fact_distrib__sup__le, fact_Int__lower2, fact_subset__Un__eq, fact_le__iff__sup, fact_sup_Oassoc, fact_DomainP__Domain__eq, fact_in__below, fact_Int__absorb, fact_ord__le__eq__trans, fact_le__infE, fact_all__not__in__conv, fact_mlex__leq, fact_set__mp, fact_inf__sup__absorb, fact_DomainP_Ointros, fact_funcset__compose, fact_accp__downward, fact_mktop__Lin, fact_wfrec__rel_Oequations, fact_r__r__into__trancl, fact_extensional__funcset__empty__range, fact_Range__Id__on, fact_Times__Un__distrib1, fact_total__on__def, fact_fun__upd__idem__iff, fact_Un__Diff__cancel, fact_le__iff__inf, fact_SigmaE, fact_bex__Un, fact_inf_Ocommute, fact_inf__sup__aci_I8_J, fact_inf__greatest, fact_sup__ge1, fact_Times__eq__cancel2, fact_sup__inf__distrib2, fact_sup1CI, fact_Nitpick_Orefl_H__def, fact_Pair__inject, fact_pred__subset__eq, fact_Range__iff, arity_HOL__Obool__Lattices_Odistrib__lattice, arity_Nat__Onat__Orderings_Obot, fact_set__eq__subset, fact_sup2E, fact_rtrancl__into__trancl2, fact_acyclic__insert, fact_Un__Int__assoc__eq, fact_subset__refl, fact_ext, fact_rtranclp__sup__rtranclp, help_c__fNot__2, fact_RangeP_Ointros, fact_inf__Int__eq2, fact_internal__split__conv, arity_fun__Orderings_Oord, fact_equalityI, fact_inf__le1, fact_Sigma__Int__distrib2, fact_le__supE, fact_inf1D1, arity_fun__Orderings_Obot, fact_empty__iff, fact_single__valued__confluent, fact_le__infI, fact_RangeP__Range__eq, fact_linorder__le__cases, fact_inf__apply, fact_assms_I3_J, fact_Id__on__eqI, fact_acyclic__def, fact_sup__Un__eq, fact_Diff__Int, fact_sup__idem, fact_fun__upd__upd, fact_Int__commute, fact_Sigma__Int__distrib1, arity_Nat__Onat__Orderings_Olinorder, fact_PiE, fact_rtrancl__induct2, fact_rtrancl__trancl__absorb, fact_compose__def, fact_inf__mono, fact_trancl__range, fact_sup__mono, fact_sup_Oidem, fact_refl__onD1, fact_Pi__eq__empty, fact_total__on__empty, fact_insert__ident, fact_acyclic__subset, fact_curryD, fact_Un__absorb, fact_subset__empty, fact_singletonE, fact_IntD2, fact_trancl_Or__into__trancl, fact_trancl__into__rtrancl, fact_rtrancl__Un__subset, fact_rtrancl__eq__or__trancl, help_c__COMBB__1, arity_HOL__Obool__Lattices_Obounded__lattice__bot, fact_extensional__subset, fact_funcset__id, fact_set__rev__mp, fact_tranclD, fact_Domain__iff, fact_Int__mono, fact_trancl__subset__Sigma__aux, fact_SigmaI, fact_mem__Sigma__iff, fact_acc__downwards__aux, fact_Un__empty__right, fact_DiffI, fact_inf__absorb2, fact_eq__mem__trans, fact_refl__onI, fact_rtrancl__induct, fact_sup__commute, fact_mlex__prod__def, fact_RangeP_Oequations, fact__096ALL_AP_058Prof_O_AALL_AP_H_058Prof_O_AALL_Aa_Ab_O_A_IALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_J_J_A_N_N_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_J_096, fact_rev__predicate2D, fact_linorder__linear, fact_trancl__into__trancl2, fact_single__valuedI, fact_Un__absorb2, fact_Int__insert__right__if1, fact_rtranclp__mono, fact_single__valued__def, fact_accp_Osimps, fact_trancl__rtrancl__absorb, arity_HOL__Obool__Lattices_Osemilattice__inf, fact_DomainE, fact_Domain__Int__subset, fact_insert__times__insert, fact_subset__insertI2, fact_UnCI, fact_Int__absorb1, fact_rev__predicate1D, fact_restrict__apply, fact_inf__sup__aci_I3_J, fact_ball__Un, fact_Un__upper1, fact_refl__on__Int, fact_in__lex__prod, fact_rtranclp__subset, fact_inf__sup__aci_I5_J, fact_SigmaD2, fact_Domain__Id__on, fact_cuts__eq, fact_inf_Oleft__idem, fact__096P_A_058_AProf_096, fact_converse__rtranclp__into__rtranclp, fact_equalityE, fact_in__rel__def, fact_inf__sup__ord_I4_J, fact_le__sup__iff, fact_Int__insert__left__if0, fact_inf__sup__distrib1, fact_empty__subsetI, fact_accp__acc__eq, fact_Pair__eq, fact_restrict__in__funcset, fact_inf__assoc, fact_rtrancl_Ortrancl__into__rtrancl, fact_rtranclE, fact_Lin__irrefl, fact_insert__mono, fact_sup_Ocommute, fact_Sigma__Un__distrib2, fact_fun__upd__def, fact_Un__Diff__cancel2, fact_Range__Un__eq, fact_inf__le2, fact_accp__downwards__aux, fact_fun__upd__twist, fact_equalityCE, fact_r__into__rtrancl, help_c__COMBK__1, fact_Nitpick_Owf__wfrec_H__def, fact_restrict__def, fact_rtrancl__into__trancl1, fact_Un__iff, fact_Not__Domain__rtrancl, fact_rtrancl__idemp, fact_Diff__insert2, fact_IntI, fact_subsetD, fact_Diff__Un, fact_above__Lin, fact_Un__Diff, fact_funcsetI, fact_u, fact_sup1E, fact_inf__sup__aci_I7_J, fact_inf__sup__ord_I3_J, fact_d1_I2_J, fact_trancl__rtrancl__trancl, fact_Id__on__empty, fact_Int__empty__right, fact_dictatorI, fact_inf__sup__aci_I6_J, fact_trancl__subset__Field2, fact_in__inv__image, fact_the__elem__eq, fact_insertE, fact_sup__inf__distrib1, fact_acyclicI, fact_acc__downward, fact_Range__empty__iff, fact_r__into__rtranclp, arity_fun__Lattices_Obounded__lattice__bot, fact_Range__insert, fact_rtranclp_Oequations_I2_J, fact_Sigma__mono, fact_Un__commute, fact_eqelem__imp__iff, fact_inf__sup__aci_I2_J, arity_fun__Lattices_Odistrib__lattice, fact_sup__bot__right, fact_Int__greatest, fact_Un__least, fact_curryI, fact_subset__trans, fact_IntE, fact_sup__absorb2, arity_HOL__Obool__Orderings_Obot, fact_pred__equals__eq, fact_Int__left__absorb, fact_le__infI1, fact_Un__upper2, fact_compose__eq, fact_rtranclp__rtrancl__eq, fact_Int__iff, fact_Un__left__absorb, fact_rtranclp__idemp, fact_Times__empty, fact__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096, fact_SigmaD1, fact_IntD1, fact_refl__on__def, fact_sup_Oleft__idem, fact_mem__def, fact_refl__on__Id__on, fact_Un__Int__distrib, fact_sup_Oleft__commute, fact_UnE, fact_Field__insert, fact_rtrancl__trancl__trancl, fact_inf__sup__aci_I1_J, fact_wfrec__rel_Osimps, fact_pred__subset__eq2, fact_inf__idem, fact_trancl__mono, fact_sup2CI, fact_inf__bot__left, fact_ord__eq__le__trans, fact_not__acc__down, fact_doubleton__eq__iff, fact_rtranclp__r__diff__Id, fact_Un__assoc, fact_rtranclp_Ortrancl__refl, fact_const__Lin__Prof, fact_disjoint__iff__not__equal, fact_Field__def, arity_HOL__Obool__Lattices_Obounded__lattice, fact_restrict__extensional, fact_trancl__domain, fact_single__valuedD, arity_fun__Lattices_Obounded__lattice, fact_Sigma__empty2
% 178.58/40.76 % No. of inferences in proof: 1143
% 178.58/40.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 40229 ms resp. 39636 ms w/o parsing
% 179.29/41.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 179.29/41.04 % [INFO] Killing All external provers ...
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