TSTP Solution File: SCT006-1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT006-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 11:50:03 EDT 2023
% Result : Unsatisfiable 15.87s 4.08s
% Output : Refutation 16.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 744
% Syntax : Number of formulae : 1399 ( 311 unt; 90 typ; 0 def)
% Number of atoms : 3007 ( 680 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 23720 (1572 ~;1698 |; 0 &;20450 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 245 ( 245 >; 0 *; 0 +; 0 <<)
% Number of symbols : 92 ( 90 usr; 7 con; 0-9 aty)
% Number of variables : 5000 ( 0 ^;5000 !; 0 ?;5000 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_in_type,type,
c_in: $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $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(tc_bool_type,type,
tc_bool: $i ).
thf(c_Arrow__Order__Mirabelle_OLin_type,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_Lattices_Obounded__lattice_type,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(class_Lattices_Olower__semilattice_type,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Lattices_Oupper__semilattice_type,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(class_Complete__Lattice_Ocomplete__lattice_type,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_Complete__Lattice_OInf__class_OInf_type,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
thf(class_Lattices_Odistrib__lattice_type,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(c_Collect_type,type,
c_Collect: $i > $i > $i ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_Complete__Lattice_OSup__class_OSup_type,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(c_Fun_Oinj__on_type,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(c_Fun_Ofun__upd_type,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(class_HOL_Oord_type,type,
class_HOL_Oord: $i > $o ).
thf(c_Complete__Lattice_Ocomplete__lattice_type,type,
c_Complete__Lattice_Ocomplete__lattice: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
thf(c_ATP__Linkup_Osko__Set__XbexI__1__1_type,type,
c_ATP__Linkup_Osko__Set__XbexI__1__1: $i > $i > $i > $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oequiv_type,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(c_SetInterval_Oord_OgreaterThanAtMost_type,type,
c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_type,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1_type,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1: $i > $i > $i > $i > $i ).
thf(c_Set_Ovimage_type,type,
c_Set_Ovimage: $i > $i > $i > $i > $i ).
thf(c_FuncSet_OPi_type,type,
c_FuncSet_OPi: $i > $i > $i > $i > $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_FuncSet_Osko__FuncSet__XfuncsetI__1__1_type,type,
c_FuncSet_Osko__FuncSet__XfuncsetI__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3_type,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3: $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oquotient_type,type,
c_Equiv__Relations_Oquotient: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__Xbspec__1__1_type,type,
c_ATP__Linkup_Osko__Set__Xbspec__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__XbexE__1__1_type,type,
c_ATP__Linkup_Osko__Set__XbexE__1__1: $i > $i > $i > $i ).
thf(c_Typedef_Otype__definition_type,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Set__XballE__1__1_type,type,
c_ATP__Linkup_Osko__Set__XballE__1__1: $i > $i > $i > $i ).
thf(c_HOL_Oundefined_type,type,
c_HOL_Oundefined: $i > $i ).
thf(c_FuncSet_Oextensional_type,type,
c_FuncSet_Oextensional: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OgreaterThan_type,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeastLessThan_type,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(c_Set_OPow_type,type,
c_Set_OPow: $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeastAtMost_type,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i > $i ).
thf(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(c_SetInterval_Oord_OgreaterThanLessThan_type,type,
c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).
thf(class_Lattices_Oboolean__algebra_type,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(c_Fun_Ooverride__on_type,type,
c_Fun_Ooverride__on: $i > $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__add_type,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(c_Finite__Set_Ofold__graph_type,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Set__XbexCI__1__1_type,type,
c_ATP__Linkup_Osko__Set__XbexCI__1__1: $i > $i > $i > $i ).
thf(c_FuncSet_Osko__FuncSet__XPi__I__1__1_type,type,
c_FuncSet_Osko__FuncSet__XPi__I__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Osetsum_type,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1_type,type,
c_FuncSet_Osko__FuncSet__XPi__I_H__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1_type,type,
c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1_type,type,
c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1_type,type,
c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1: $i > $i > $i > $i ).
thf(c_List_Osko__Equiv__Relations__XquotientE__1__1_type,type,
c_List_Osko__Equiv__Relations__XquotientE__1__1: $i > $i > $i > $i > $i ).
thf(c_Not_type,type,
c_Not: $i ).
thf(c_Order__Relation_Owell__order__on_type,type,
c_Order__Relation_Owell__order__on: $i > $i > $i > $o ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(v_sko__CHAINED__1_type,type,
v_sko__CHAINED__1: $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3_type,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1_type,type,
c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1: $i > $i > $i > $i ).
thf(c_FuncSet_Osko__FuncSet__XextensionalityI__1__1_type,type,
c_FuncSet_Osko__FuncSet__XextensionalityI__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OlessThan_type,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
thf(c_Nitpick_Ofold__graph_H_type,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3_type,type,
c_ATP__Linkup_Osko__Set__Xbex__Un__1__3: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatMost_type,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(892,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(294,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
thf(1322,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(477,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ E @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ E @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_3) ).
thf(1718,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ E @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ E @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(646,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__Diff__eq_0) ).
thf(2094,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(366,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(1469,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(441,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 @ D @ A @ B @ C @ E ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ E ) ) @ B ) @ ( c_FuncSet_Oextensional @ D @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ E ) ) @ A ) @ ( c_FuncSet_Oextensional @ D @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_extensionalityI_0) ).
thf(1633,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 @ D @ A @ B @ C @ E ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ E ) ) @ B ) @ ( c_FuncSet_Oextensional @ D @ C @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ E ) ) @ A ) @ ( c_FuncSet_Oextensional @ D @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(635,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(2072,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(1105,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(846,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).
thf(1031,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(557,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(1899,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(530,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__sup_0) ).
thf(1840,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(534,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(1850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(595,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ B ) ) @ C ) @ ( c_FuncSet_OPi @ D @ E @ A @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ D @ E @ C @ A @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pi__I_0) ).
thf(1982,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ B ) ) @ C ) @ ( c_FuncSet_OPi @ D @ E @ A @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ D @ E @ C @ A @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(1179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(403,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ D @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__I_0) ).
thf(1554,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ D @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(380,axiom,
! [B: $i,A: $i] :
( ( c_Collect @ ( c_COMBB @ c_Not @ A @ tc_bool @ tc_bool @ B ) @ B )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Collect @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__neg__eq_0) ).
thf(1501,plain,
! [B: $i,A: $i] :
( ( c_Collect @ ( c_COMBB @ c_Not @ A @ tc_bool @ tc_bool @ B ) @ B )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Collect @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ C @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__empty2_0) ).
thf(1168,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ C @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( c_Collect @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
thf(760,plain,
! [B: $i,A: $i] :
( ( c_Collect @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(652,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(2109,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( c_Set_OPow @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PowD_0) ).
thf(1454,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( c_Set_OPow @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(666,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(520,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(549,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
thf(1882,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(176,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(1068,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(434,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageI_0) ).
thf(1618,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(332,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Collect @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectI_0) ).
thf(1401,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Collect @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(398,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(1544,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(481,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_Relation_OImage @ B @ ( c_Set_Oinsert @ ( c_List_Osko__Equiv__Relations__XquotientE__1__1 @ C @ A @ B @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ ( c_Equiv__Relations_Oquotient @ C @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotientE_0) ).
thf(1728,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_Relation_OImage @ B @ ( c_Set_Oinsert @ ( c_List_Osko__Equiv__Relations__XquotientE__1__1 @ C @ A @ B @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ ( c_Equiv__Relations_Oquotient @ C @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1269,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(536,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1855,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(638,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(2077,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ B @ D @ A ) @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ B @ D @ A ) @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(762,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(424,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Set_Oimage @ B @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1596,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Set_Oimage @ B @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(335,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( c_Set_Oimage @ E @ C @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(1406,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( c_Set_Oimage @ E @ C @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(353,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(1443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(516,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( c_Equiv__Relations_Oquotient @ D @ E @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( c_Equiv__Relations_Oquotient @ D @ E @ C ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ D @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotient__disj_0) ).
thf(1808,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( c_Equiv__Relations_Oquotient @ D @ E @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( c_Equiv__Relations_Oquotient @ D @ E @ C ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ D @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(878,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(655,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(590,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1971,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(510,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(1793,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(164,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ ( tc_fun @ E @ tc_bool ) ) ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ B @ H ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ H ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP2__I_0) ).
thf(1041,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ ( tc_fun @ E @ tc_bool ) ) ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ B @ H ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ H ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(861,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(471,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ A @ B ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ) )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).
thf(1705,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ A @ B ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ) )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(450,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
thf(1655,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(618,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ D @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__Un_6) ).
thf(2035,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ D @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(484,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ D @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__iff_2) ).
thf(1735,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ D @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(542,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_InterD_0) ).
thf(1867,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(544,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(1872,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(296,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(1327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(945,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(174,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ B ) ) @ ( c_Pair @ A @ D @ B @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ A ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_1) ).
thf(1063,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ B ) ) @ ( c_Pair @ A @ D @ B @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ A ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(621,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
thf(2042,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(220,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(1164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(603,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(1999,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(566,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
thf(1919,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(598,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(496,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
thf(1761,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(303,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(1342,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(913,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(623,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(2046,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(564,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Collect @ A @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
thf(1914,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Collect @ A @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(326,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ A @ B @ ( c_COMBC @ C @ D @ D @ tc_bool ) @ ( c_COMBC @ E @ D @ D @ tc_bool ) @ F @ G @ H @ I @ D )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ A @ C @ E @ G @ F @ I @ H @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
thf(1391,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ A @ B @ ( c_COMBC @ C @ D @ D @ tc_bool ) @ ( c_COMBC @ E @ D @ D @ tc_bool ) @ F @ G @ H @ I @ D )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ A @ C @ E @ G @ F @ I @ H @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(352,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnionE_0) ).
thf(1441,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ B @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(612,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_Relation_Oconverse @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__in__Lin_0) ).
thf(2020,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_Relation_Oconverse @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(885,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(431,axiom,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(1613,plain,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(573,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
= C )
| ~ ( c_Typedef_Otype__definition @ B @ A @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__definition_ORep__inverse_0) ).
thf(1935,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
= C )
| ~ ( c_Typedef_Otype__definition @ B @ A @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(567,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__empty_0) ).
thf(1921,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(311,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
thf(1359,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(324,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Osetsum @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ tc_nat )
= ( c_Finite__Set_Osetsum @ A @ B @ D @ tc_nat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1__nat_1) ).
thf(1386,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Osetsum @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ tc_nat )
= ( c_Finite__Set_Osetsum @ A @ B @ D @ tc_nat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(641,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ C ) @ C @ C @ tc_bool ) @ A ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__def_0) ).
thf(2082,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ C ) @ C @ C @ tc_bool ) @ A ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(314,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Collect @ B @ C ) @ D @ C )
= ( c_Collect @ ( c_COMBB @ B @ A @ C @ tc_bool @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Collect__eq_0) ).
thf(1366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Collect @ B @ C ) @ D @ C )
= ( c_Collect @ ( c_COMBB @ B @ A @ C @ tc_bool @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(588,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(1967,plain,
class_Lattices_Oupper__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(514,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
thf(1803,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(470,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1703,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(372,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(1482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(1254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(347,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Relation_OImage @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) ) @ ( c_Equiv__Relations_Oquotient @ D @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotientI_0) ).
thf(1430,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Relation_OImage @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) ) @ ( c_Equiv__Relations_Oquotient @ D @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(719,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).
thf(1313,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(600,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ ( c_Relation_Oconverse @ E @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ A ) ) @ ( c_Pair @ D @ C @ B @ A ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__iff_1) ).
thf(1992,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ ( c_Relation_Oconverse @ E @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ A ) ) @ ( c_Pair @ D @ C @ B @ A ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(170,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_5) ).
thf(1055,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(30,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(724,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(495,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(1760,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(283,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
thf(1298,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(539,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexE_1) ).
thf(1860,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(267,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(1264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(384,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1511,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(751,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(934,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(233,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OatLeastAtMost @ A @ E @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_1) ).
thf(1191,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OatLeastAtMost @ A @ E @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(172,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ A @ G @ H @ I @ J @ K @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
thf(1059,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ A @ G @ H @ I @ J @ K @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(205,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(1132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(83,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(853,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(553,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_0) ).
thf(1892,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(385,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ E @ A ) ) @ B ) @ ( c_FuncSet_OPi @ F @ ( c_COMBK @ D @ ( tc_fun @ A @ tc_bool ) @ E ) @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funcset__mem_0) ).
thf(1514,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ E @ A ) ) @ B ) @ ( c_FuncSet_OPi @ F @ ( c_COMBK @ D @ ( tc_fun @ A @ tc_bool ) @ E ) @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(624,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(2049,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(330,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1398,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
thf(1115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(410,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(1568,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(1232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(293,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).
thf(1319,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(552,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ D @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__insert_0) ).
thf(1890,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ D @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(969,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(305,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexCI_0) ).
thf(1347,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(1013,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(49,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(770,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(614,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( c_COMBK @ C @ A @ D ) @ D @ A )
= C )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP__const_0) ).
thf(2024,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( c_COMBK @ C @ A @ D ) @ D @ A )
= C )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(444,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
thf(1641,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(519,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
thf(1815,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(377,axiom,
! [B: $i,A: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_OPow @ A @ B ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__Pow__eq_0) ).
thf(1494,plain,
! [B: $i,A: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_OPow @ A @ B ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(312,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1362,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(586,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Relation_OImage @ ( c_Relation_Oconverse @ A @ C @ D ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ E ) @ D @ C ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__subset__eq_1) ).
thf(1963,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Relation_OImage @ ( c_Relation_Oconverse @ A @ C @ D ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ E ) @ D @ C ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(375,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_1) ).
thf(1489,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(113,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(924,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(364,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).
thf(1465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(285,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_6) ).
thf(1302,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(517,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(1811,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).
thf(1373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(1136,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(525,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_2) ).
thf(1828,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(460,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__inf_0) ).
thf(1677,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(584,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1960,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(416,axiom,
! [B: $i,A: $i] :
( ( c_Collect @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
thf(1581,plain,
! [B: $i,A: $i] :
( ( c_Collect @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(475,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( c_Set_Oimage @ E @ C @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(1714,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( c_Set_Oimage @ E @ C @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(615,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(2027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(537,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1858,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(541,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
thf(1864,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(322,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_OPow @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pow__top_0) ).
thf(1383,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_OPow @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(1020,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(229,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ F ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ B @ F @ E @ A ) @ D @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(1183,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ F ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ B @ F @ E @ A ) @ D @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(277,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_0) ).
thf(1283,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(636,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__eq_0) ).
thf(2073,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(981,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(531,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(1843,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(687,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(570,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(1928,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1447,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(866,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(328,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(1394,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(390,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ ( c_Set_Ovimage @ A @ E @ C @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
thf(1526,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ ( c_Set_Ovimage @ A @ E @ C @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(307,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
thf(1351,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(660,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(304,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ F ) @ D ) @ C ) )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) @ ( tc_fun @ F @ tc_bool ) ) @ E @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).
thf(1345,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ F ) @ D ) @ C ) )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) @ ( tc_fun @ F @ tc_bool ) ) @ E @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1600,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(1521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(592,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
thf(1975,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(511,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Oboolean__algebra @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
thf(1796,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Oboolean__algebra @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(1072,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(199,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( c_Typedef_Otype__definition @ F @ A @ E @ G @ D )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__definition_OAbs__inject_0) ).
thf(1119,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( c_Typedef_Otype__definition @ F @ A @ E @ G @ D )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(436,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(1622,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(774,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(650,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(2103,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(334,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(1405,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(576,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ F ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ A @ E @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
thf(1943,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ F ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ F @ A @ E @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(238,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(1201,plain,
class_Lattices_Obounded__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(1697,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(1242,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(448,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_11) ).
thf(1651,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(608,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(2011,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(241,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1206,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(465,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).
thf(1691,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1438,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Complete__Lattice_OSup__class_OSup @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__upper_0) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Complete__Lattice_OSup__class_OSup @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(505,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ B @ C @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnionE_1) ).
thf(1783,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ B @ C @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1311,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(499,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1768,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(714,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(630,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_4) ).
thf(2061,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(1636,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(167,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ B ) ) @ C ) @ ( c_FuncSet_OPi @ D @ ( c_COMBK @ E @ ( tc_fun @ B @ tc_bool ) @ A ) @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( hAPP @ C @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ D @ E @ C @ A @ B ) ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funcsetI_1) ).
thf(1047,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ B ) ) @ C ) @ ( c_FuncSet_OPi @ D @ ( c_COMBK @ E @ ( tc_fun @ B @ tc_bool ) @ A ) @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( hAPP @ C @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ D @ E @ C @ A @ B ) ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(798,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
thf(1057,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).
thf(1274,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(249,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
thf(1223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__constant_1) ).
thf(1091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(952,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(387,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_Relation_Oconverse @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ c_Arrow__Order__Mirabelle_OLin ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__in__Lin_1) ).
thf(1519,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_Relation_Oconverse @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ c_Arrow__Order__Mirabelle_OLin ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(309,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ B ) ) @ C ) @ ( c_FuncSet_OPi @ D @ E @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( hAPP @ C @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ D @ E @ C @ A @ B ) ) ) @ ( hAPP @ E @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ D @ E @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pi__I_1) ).
thf(1355,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ B ) ) @ C ) @ ( c_FuncSet_OPi @ D @ E @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( hAPP @ C @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ D @ E @ C @ A @ B ) ) ) @ ( hAPP @ E @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ D @ E @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(455,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OlessThan @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_1) ).
thf(1666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OlessThan @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(374,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(1487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ B @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(693,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ B @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(256,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ C @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_2) ).
thf(1238,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ C @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(1560,plain,
! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(479,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Collect @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectD_0) ).
thf(1723,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Collect @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(107,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(910,plain,
class_Lattices_Olattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(411,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_fun @ D @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
thf(1570,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_fun @ D @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B )
!= ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).
thf(1174,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B )
!= ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(491,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1751,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(69,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(820,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(523,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).
thf(1824,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(788,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(316,axiom,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(1370,plain,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(617,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
thf(2032,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(67,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(815,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(343,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ ( c_Set_Oinsert @ ( hAPP @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
thf(1423,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ ( c_Set_Oinsert @ ( hAPP @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(574,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(1938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(589,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
thf(1968,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(580,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(1951,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI2_0) ).
thf(830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(243,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OatLeastLessThan @ C @ D @ E @ F @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_2) ).
thf(1210,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OatLeastLessThan @ C @ D @ E @ F @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(757,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ D @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ C @ D @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ballE_0) ).
thf(1128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ D @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ C @ D @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(276,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(1281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(562,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(1910,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(193,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageE_0) ).
thf(1106,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(551,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ D @ B @ A @ A ) ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ C @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
thf(1888,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ D @ B @ A @ A ) ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ C @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(282,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(1296,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(5,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(665,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(633,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ B @ A ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
thf(2068,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ B @ A ) @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(437,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(1624,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(528,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThan__iff_0) ).
thf(1836,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(507,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( c_COMBB @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) @ F ) @ F @ ( tc_fun @ E @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ C @ A @ F @ D ) @ B @ D @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I10_J_0) ).
thf(1787,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( c_COMBB @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) @ F ) @ F @ ( tc_fun @ E @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ C @ A @ F @ D ) @ B @ D @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(181,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_8) ).
thf(1079,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(157,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ C @ D @ E @ F @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThanAtMost__iff_2) ).
thf(1027,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ C @ D @ E @ F @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(682,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(235,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(1195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(654,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexCI_2) ).
thf(2112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(280,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ D @ F )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(1291,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ D @ F )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(710,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(413,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(1573,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(133,axiom,
class_Lattices_Olower__semilattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(974,plain,
class_Lattices_Olower__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(649,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(2100,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(271,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(1270,plain,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(319,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1375,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(725,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(345,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B )
!= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ A ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ C @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ B ) ) @ ( c_Pair @ A @ D @ B @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_0) ).
thf(1425,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B )
!= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ A ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ C @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ B ) ) @ ( c_Pair @ A @ D @ B @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(547,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1878,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(1138,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(869,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(493,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
thf(1755,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI1_0) ).
thf(989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(422,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ B @ C @ D )
= ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_in @ D ) @ A @ D @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ C ) @ C @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__def_0) ).
thf(1592,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ B @ C @ D )
= ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_in @ D ) @ A @ D @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ C ) @ C @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(742,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(697,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(254,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(91,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(874,plain,
class_Lattices_Oupper__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(210,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_7) ).
thf(1143,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(394,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Relation_OImage @ ( c_Relation_Oconverse @ C @ B @ D ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ E ) @ D @ B ) ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OImage @ C @ A @ B @ D ) @ E @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__subset__eq_0) ).
thf(1534,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Relation_OImage @ ( c_Relation_Oconverse @ C @ B @ D ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ E ) @ D @ B ) ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OImage @ C @ A @ B @ D ) @ E @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(153,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).
thf(1017,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(581,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
thf(1953,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(195,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ D ) ) @ A ) @ ( c_FuncSet_OPi @ B @ ( c_COMBK @ E @ ( tc_fun @ D @ tc_bool ) @ C ) @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funcset__image_0) ).
thf(1111,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ D ) ) @ A ) @ ( c_FuncSet_OPi @ B @ ( c_COMBK @ E @ ( tc_fun @ D @ tc_bool ) @ C ) @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(251,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1227,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(379,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(1498,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(419,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(1587,plain,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(188,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageI2_0) ).
thf(1096,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(458,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(1672,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(462,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(1683,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(297,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
thf(1329,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
thf(1160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(452,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
thf(1659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(669,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(344,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
thf(1424,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(640,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(2080,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__binary_0) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(509,axiom,
! [B: $i,A: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
thf(1791,plain,
! [B: $i,A: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
thf(1214,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(445,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1644,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(488,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
thf(1744,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(341,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1419,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(486,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(1739,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(1461,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(901,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(179,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_10) ).
thf(1075,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(679,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(1039,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(524,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
thf(1825,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(502,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1776,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(1588,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(357,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__bexI_1) ).
thf(1451,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(456,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
thf(1668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(572,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(1932,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(606,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ C ) @ D @ C @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__negf_0) ).
thf(2006,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ C ) @ D @ C @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(578,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1947,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(596,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ B @ C @ A @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ ( hAPP @ C @ G ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ G ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__UN_4) ).
thf(1984,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ B @ C @ A @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ ( hAPP @ C @ G ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ G ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
thf(1002,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(545,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ooverride__on @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_override__on__emptyset_0) ).
thf(1874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ooverride__on @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(478,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 @ B @ A @ C @ D @ E ) )
!= ( hAPP @ C @ ( c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 @ B @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ D @ E ) ) @ C ) @ ( c_FuncSet_Oextensional @ B @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ D @ E ) ) @ A ) @ ( c_FuncSet_Oextensional @ B @ D @ E ) ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_extensionalityI_1) ).
thf(1720,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 @ B @ A @ C @ D @ E ) )
!= ( hAPP @ C @ ( c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 @ B @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ D @ E ) ) @ C ) @ ( c_FuncSet_Oextensional @ B @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ D @ E ) ) @ A ) @ ( c_FuncSet_Oextensional @ B @ D @ E ) ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(594,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(1979,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(327,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(1393,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(438,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
thf(1627,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(1150,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(370,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(1478,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1249,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) )
= ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
thf(1539,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) )
= ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(360,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E )
!= A )
| ( ( hAPP @ A @ B )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
thf(1456,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E )
!= A )
| ( ( hAPP @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(268,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Set_OPow @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pow__bottom_0) ).
thf(1266,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Set_OPow @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(526,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).
thf(1831,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(984,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(911,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(626,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OlessThan @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_0) ).
thf(2052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OlessThan @ A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(260,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(1246,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(1333,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(349,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(1434,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(503,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(1779,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(921,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(1170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(555,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( hAPP @ F @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ D ) ) @ E ) @ ( c_FuncSet_OPi @ C @ F @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PiE_0) ).
thf(1895,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ E @ B ) ) @ ( hAPP @ F @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ D ) ) @ E ) @ ( c_FuncSet_OPi @ C @ F @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(1185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(602,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).
thf(1996,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(483,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ( B = C )
| ~ ( c_Fun_Oinj__on @ A @ E @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(1732,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ( B = C )
| ~ ( c_Fun_Oinj__on @ A @ E @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ A ) @ A @ A @ tc_bool ) @ B ) @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv_0) ).
thf(1202,plain,
! [B: $i,A: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ A ) @ A @ A @ tc_bool ) @ B ) @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__Un_0) ).
thf(1086,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(938,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(408,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(1563,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(657,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(765,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(1712,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(532,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeastAtMost @ A @ B @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_0) ).
thf(1846,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeastAtMost @ A @ B @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(278,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ D @ E @ C @ C ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( c_Equiv__Relations_Oquotient @ G @ F @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( c_Equiv__Relations_Oquotient @ G @ F @ C ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ G @ F @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotient__eqI_0) ).
thf(1286,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ D @ E @ C @ C ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( c_Equiv__Relations_Oquotient @ G @ F @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( c_Equiv__Relations_Oquotient @ G @ F @ C ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ G @ F @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(1035,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(231,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__Un_0) ).
thf(1187,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(674,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(454,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1663,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(644,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ B @ D @ E )
| ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).
thf(2089,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ B @ D @ E )
| ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI2_0) ).
thf(906,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(604,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oinsert @ C @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ F @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).
thf(2001,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oinsert @ C @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ F @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(497,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).
thf(1764,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(461,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
thf(1680,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).
thf(1103,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(1219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(489,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(1747,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(400,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ A ) ) @ ( c_Pair @ D @ C @ B @ A ) ) @ ( c_Relation_Oconverse @ E @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseD_0) ).
thf(1548,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ A ) ) @ ( c_Pair @ D @ C @ B @ A ) ) @ ( c_Relation_Oconverse @ E @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(745,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(689,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Equiv__Relations_Oquotient @ A @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_Equiv__Relations_Oequiv @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__quotient_0) ).
thf(1278,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Equiv__Relations_Oquotient @ A @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_Equiv__Relations_Oequiv @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(560,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(1906,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(440,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).
thf(1631,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(733,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OgreaterThan @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThan__iff_1) ).
thf(1154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OgreaterThan @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( c_Collect @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_1) ).
thf(1007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( c_Collect @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(843,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(435,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ C @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
thf(1620,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ D @ A @ A ) ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ C @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(492,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( B = A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_notin__Lin__iff_0) ).
thf(1752,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( B = A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(571,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(1929,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(610,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__subset__eq_1) ).
thf(2016,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(469,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(1701,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(587,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(1965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(201,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ E @ A @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_1) ).
thf(1124,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ E @ A @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
thf(1256,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(904,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(975,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(1615,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).
thf(1389,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(875,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(826,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(958,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(333,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OatLeastAtMost @ C @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_2) ).
thf(1403,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OatLeastAtMost @ C @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(346,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).
thf(1428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
thf(1503,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(936,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(616,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
thf(2029,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(472,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(1707,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).
thf(1371,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__eq_0) ).
thf(1258,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(123,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(947,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(459,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1675,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(672,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(556,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(1897,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(804,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(639,axiom,
class_Lattices_Oboolean__algebra @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
thf(2079,plain,
class_Lattices_Oboolean__algebra @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(642,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_3) ).
thf(2084,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(554,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).
thf(1894,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(306,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(1349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(397,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(1542,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(200,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(1122,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(412,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__trans_0) ).
thf(1571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(287,axiom,
class_Lattices_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(1307,plain,
class_Lattices_Odistrib__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(632,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Collect @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).
thf(2065,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Collect @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(535,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(1853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(336,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(1408,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(784,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(198,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(1117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(515,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ D ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
thf(1806,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ D ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexI_0) ).
thf(1011,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(376,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Oimage @ A @ F @ D @ E ) ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).
thf(1492,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Oimage @ A @ F @ D @ E ) ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(427,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ A ) ) @ ( c_Pair @ F @ B @ E @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_2) ).
thf(1603,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ A ) ) @ ( c_Pair @ F @ B @ E @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(500,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Typedef_Otype__definition @ A @ D @ E @ F @ G )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__definition_ORep__inject_0) ).
thf(1771,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Typedef_Otype__definition @ A @ D @ E @ F @ G )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(880,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(1043,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(513,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).
thf(1801,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(98,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B @ F @ D @ E )
= ( c_Fun_Ofun__upd @ A @ B @ F @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
thf(890,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B @ F @ D @ E )
= ( c_Fun_Ofun__upd @ A @ B @ F @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1471,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(301,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1339,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(482,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1731,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(1162,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(540,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(1862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(700,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(110,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(915,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(404,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(1556,plain,
class_Lattices_Olower__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(943,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(1061,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(521,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).
thf(1820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(1688,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(858,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(405,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( c_Typedef_Otype__definition @ A @ B @ E @ F @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__definition_OAbs__inverse_0) ).
thf(1557,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( c_Typedef_Otype__definition @ A @ B @ E @ F @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(529,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).
thf(1838,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1325,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(158,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ A @ E @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_0) ).
thf(1029,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ A @ E @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(895,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(226,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeastLessThan @ A @ E @ B @ F @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_0) ).
thf(1177,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeastLessThan @ A @ E @ B @ F @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(321,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(1381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(329,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ B ) ) @ C ) @ ( c_FuncSet_OPi @ D @ E @ A @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ D @ E @ C @ A @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pi__I_H_0) ).
thf(1396,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ B ) ) @ C ) @ ( c_FuncSet_OPi @ D @ E @ A @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ D @ E @ C @ A @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(695,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(53,axiom,
class_Lattices_Odistrib__lattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(780,plain,
class_Lattices_Odistrib__lattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(883,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(1015,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(1113,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(1000,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(613,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ ( tc_fun @ E @ tc_bool ) ) ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ B @ H ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ H ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP2__iff_2) ).
thf(2022,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ ( tc_fun @ E @ tc_bool ) ) ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ B @ H ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ H ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(313,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ A @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__constant_0) ).
thf(1364,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ A @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(378,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
thf(1496,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(851,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(466,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(1694,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(137,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(983,plain,
class_HOL_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(637,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_0) ).
thf(2075,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(423,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1594,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(468,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ ( hAPP @ ( hAPP @ A @ C ) @ F ) @ E @ G )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ D @ F @ E @ G )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).
thf(1699,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ ( hAPP @ ( hAPP @ A @ C ) @ F ) @ E @ G )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ D @ F @ E @ G )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(175,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(1066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(354,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ B @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
thf(1445,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ B @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(391,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
thf(1528,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(417,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(1583,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(647,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ A @ B @ E @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_0) ).
thf(2096,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ A @ B @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).
thf(1304,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(221,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ A @ B @ C @ D ) @ E @ D @ ( tc_fun @ F @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( c_COMBB @ E @ A @ D @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ ( tc_fun @ F @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__simps_I10_J_0) ).
thf(1166,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ A @ B @ C @ D ) @ E @ D @ ( tc_fun @ F @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( c_COMBB @ E @ A @ D @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ ( tc_fun @ F @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(242,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(1208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(365,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( hBOOL @ ( hAPP @ D @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ballE_1) ).
thf(1467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( hBOOL @ ( hAPP @ D @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(663,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Complete__Lattice_OSup__class_OSup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ B @ tc_bool ) ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1 @ C @ A @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__disjoint_1) ).
thf(1420,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Complete__Lattice_OSup__class_OSup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ B @ tc_bool ) ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1 @ C @ A @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(206,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ A @ E @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ A @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_2) ).
thf(1134,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ A @ E @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ D @ A @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(182,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
thf(1081,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(599,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__bexI_0) ).
thf(1990,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(302,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inter__lower_0) ).
thf(1340,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(211,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( c_HOL_Oundefined @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ D @ C ) ) @ A ) @ ( c_FuncSet_Oextensional @ E @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_extensional__arb_0) ).
thf(1145,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( c_HOL_Oundefined @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ D @ C ) ) @ A ) @ ( c_FuncSet_Oextensional @ E @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(754,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_1) ).
thf(1049,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(627,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(2054,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(722,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI1_0) ).
thf(927,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(619,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= C )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(2037,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= C )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(812,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(383,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ B ) ) @ C ) @ ( c_FuncSet_OPi @ D @ ( c_COMBK @ E @ ( tc_fun @ B @ tc_bool ) @ A ) @ A @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ D @ E @ C @ A @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funcsetI_0) ).
thf(1509,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ B ) ) @ C ) @ ( c_FuncSet_OPi @ D @ ( c_COMBK @ E @ ( tc_fun @ B @ tc_bool ) @ A ) @ A @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 @ D @ E @ C @ A @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).
thf(1181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(836,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).
thf(1551,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(776,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(512,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(1798,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(855,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(585,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).
thf(1961,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(156,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
thf(1025,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(97,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ G @ D @ E )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ F @ G @ D @ E ) @ B @ C @ D @ E ) )
| ( B = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
thf(887,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ G @ D @ E )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ F @ G @ D @ E ) @ B @ C @ D @ E ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(409,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ B @ C @ D @ E @ A ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ ( hAPP @ C @ G ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ G ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__UN_3) ).
thf(1566,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ B @ C @ D @ E @ A ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ ( hAPP @ C @ G ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ G ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ B )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
thf(1605,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ B )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(446,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
thf(739,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(1368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(269,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Collect @ D @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_2) ).
thf(1267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Collect @ D @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(392,axiom,
c_Order__Relation_Owell__order__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ tc_bool ) ) @ v_sko__CHAINED__1 @ tc_Arrow__Order__Mirabelle_Oalt,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(1531,plain,
c_Order__Relation_Owell__order__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ tc_bool ) ) @ v_sko__CHAINED__1 @ tc_Arrow__Order__Mirabelle_Oalt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(1098,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(993,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(386,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(1516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ B @ C @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_InterI_0) ).
thf(1598,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ B @ C @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Set__Xbspec__1__1 @ D @ A @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bspec_0) ).
thf(1070,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Set__Xbspec__1__1 @ D @ A @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(872,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(705,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(216,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OatLeastLessThan @ E @ A @ F @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_1) ).
thf(1156,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OatLeastLessThan @ E @ A @ F @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(250,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(1225,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(23,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(707,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(575,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnionI_0) ).
thf(1941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(1252,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(645,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ A ) ) @ ( c_Pair @ D @ B @ E @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
thf(2092,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ A ) ) @ ( c_Pair @ D @ B @ E @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(476,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(1716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(1432,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(543,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1869,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( B = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(558,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Set_Oimage @ B @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(1901,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Set_Oimage @ B @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(622,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(2044,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplD_0) ).
thf(1130,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(300,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ B @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_override__on__apply__in_0) ).
thf(1336,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ B @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(518,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(1813,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(1300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(840,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(506,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ ( c_Relation_OImage @ E @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
thf(1785,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ ( c_Relation_OImage @ E @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(628,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(2056,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(498,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ A @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_1) ).
thf(1766,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(1536,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(155,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ A @ E @ F @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThanAtMost__iff_1) ).
thf(1023,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ A @ E @ F @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(248,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(1221,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(87,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
= ( c_Set_Oimage @ ( c_COMBB @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(864,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
= ( c_Set_Oimage @ ( c_COMBB @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(490,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(1749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(727,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(457,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ E ) )
| ~ ( c_lessequals @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).
thf(1670,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ E ) )
| ~ ( c_lessequals @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(308,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ F @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
thf(1353,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ B @ C @ A @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ F @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(582,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1955,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(373,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(1485,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(591,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
thf(1972,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(169,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ C @ I @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
thf(1052,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ C @ I @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(382,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__const_1) ).
thf(1506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ A ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(1585,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ A ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(1094,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(209,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Set_Oimage @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
thf(1140,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Set_Oimage @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Compl_0) ).
thf(1240,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(991,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(433,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(1617,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(609,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1 @ A @ B @ C ) @ A @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Complete__Lattice_OSup__class_OSup @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__disjoint_2) ).
thf(2013,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1 @ A @ B @ C ) @ A @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Complete__Lattice_OSup__class_OSup @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__Int_0) ).
thf(1459,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(579,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ ( c_Relation_Oconverse @ E @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ A ) ) @ ( c_Pair @ D @ C @ B @ A ) ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseI_0) ).
thf(1949,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ B ) ) @ ( c_Pair @ C @ D @ A @ B ) ) @ ( c_Relation_Oconverse @ E @ B @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ B @ A ) ) @ ( c_Pair @ D @ C @ B @ A ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(527,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ A ) ) @ ( c_Pair @ F @ B @ E @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
thf(1834,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ E @ A ) ) @ ( c_Pair @ F @ B @ E @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(338,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexI_1) ).
thf(1412,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(202,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(1126,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(194,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).
thf(1108,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(292,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( c_Equiv__Relations_Oquotient @ E @ F @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( c_Equiv__Relations_Oquotient @ E @ F @ A ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ F @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ D @ B @ A @ A ) ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotient__eq__iff_0) ).
thf(1316,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( c_Equiv__Relations_Oquotient @ E @ F @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( c_Equiv__Relations_Oquotient @ E @ F @ A ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ F @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ A @ A ) ) @ ( c_Pair @ D @ B @ A @ A ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(447,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__upper_0) ).
thf(1649,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(183,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ E @ B @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
thf(1084,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ E @ B @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(931,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(463,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1685,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(504,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageD_0) ).
thf(1781,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Complete__Lattice_OSup__class_OSup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C @ ( tc_fun @ B @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__disjoint_0) ).
thf(1216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Complete__Lattice_OSup__class_OSup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C @ ( tc_fun @ B @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(356,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(1448,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_OPow @ C @ A ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PowI_0) ).
thf(1189,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_OPow @ C @ A ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(653,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) )
| ( c_lessequals @ C @ B @ ( tc_fun @ D @ A ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_2) ).
thf(2110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) )
| ( c_lessequals @ C @ B @ ( tc_fun @ D @ A ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(414,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(1575,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(279,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(1453,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(129,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(963,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(369,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_List_Osko__Equiv__Relations__XquotientE__1__1 @ B @ C @ D @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( c_Equiv__Relations_Oquotient @ B @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotientE_1) ).
thf(1476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_List_Osko__Equiv__Relations__XquotientE__1__1 @ B @ C @ D @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( c_Equiv__Relations_Oquotient @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(443,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1639,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(559,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).
thf(1903,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexE_0) ).
thf(1101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ B @ C @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(389,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(1523,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(781,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(143,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
thf(995,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(274,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).
thf(1276,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(1590,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(648,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_InterI_1) ).
thf(2098,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(439,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(1629,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(605,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ D @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__Un_4) ).
thf(2004,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ D @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(259,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_9) ).
thf(1244,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ A @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ D @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(522,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( c_Typedef_Otype__definition @ B @ E @ D @ F @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__definition_ORep_0) ).
thf(1822,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( c_Typedef_Otype__definition @ B @ E @ D @ F @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(731,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(786,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(607,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).
thf(2009,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(1294,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(288,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(1308,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(234,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).
thf(1193,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(180,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).
thf(1077,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
thf(1212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(429,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(1607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(289,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ A @ E @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_1) ).
thf(1309,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ A @ E @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(601,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubsetD_0) ).
thf(1994,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(166,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
thf(1045,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(716,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(899,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(453,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(1661,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(832,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(684,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(561,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ E @ A @ B @ F @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThanAtMost__iff_0) ).
thf(1908,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ E @ A @ B @ F @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(501,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__Un_5) ).
thf(1774,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(480,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( hAPP @ C @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
thf(1725,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( hAPP @ C @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(967,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(252,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(1229,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(399,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_0) ).
thf(1546,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(546,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__Un_7) ).
thf(1876,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ B @ C @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(597,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OatMost @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatMost__iff_1) ).
thf(1986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord_OatMost @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(212,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
thf(1148,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(494,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Finite__Set_Ofold__graph @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ A @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).
thf(1757,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Finite__Set_Ofold__graph @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ A @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1480,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(415,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ D @ F )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(1578,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ D @ F )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(583,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( ( hAPP @ B @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
thf(1957,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( ( hAPP @ B @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(950,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(75,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(835,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(790,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(625,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).
thf(2050,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(451,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(1657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(807,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(634,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(2070,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(407,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(1561,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(508,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexCI_3) ).
thf(1789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(828,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(620,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ E @ A ) ) @ B ) @ ( c_FuncSet_OPi @ F @ D @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pi__mem_0) ).
thf(2040,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ E @ A ) ) @ B ) @ ( c_FuncSet_OPi @ F @ D @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(955,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(487,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Nitpick_Ofold__graph_H @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) @ ( tc_fun @ F @ tc_bool ) ) @ E @ F @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ F ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I2_J_0) ).
thf(1742,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Nitpick_Ofold__graph_H @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) @ ( tc_fun @ F @ tc_bool ) ) @ E @ F @ G )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ F ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(350,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(538,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1859,plain,
class_HOL_Oord @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(111,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(918,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(801,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(224,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(1172,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(897,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(1410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(1033,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(473,axiom,
! [B: $i,A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(1710,plain,
! [B: $i,A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ C ) @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ C ) @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__subset__eq_0) ).
thf(1197,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ C ) @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ ( c_in @ C ) @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(960,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).
thf(1473,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(631,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
thf(2063,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(1610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(77,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(839,plain,
class_Orderings_Obot @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(593,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1977,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(266,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_override__on__apply__notin_0) ).
thf(1261,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbspec__1__1 @ D @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bspec_1) ).
thf(1152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbspec__1__1 @ D @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(393,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ B ) ) @ C ) @ ( c_FuncSet_OPi @ D @ E @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( hAPP @ C @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ D @ E @ C @ A @ B ) ) ) @ ( hAPP @ E @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ D @ E @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pi__I_H_1) ).
thf(1532,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ B ) ) @ C ) @ ( c_FuncSet_OPi @ D @ E @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( hAPP @ C @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ D @ E @ C @ A @ B ) ) ) @ ( hAPP @ E @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ D @ E @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(323,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Un_0) ).
thf(1384,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(1378,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(401,axiom,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).
thf(1550,plain,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
thf(1357,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__converse_0) ).
thf(908,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(568,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexCI_1) ).
thf(1923,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ B @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(569,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(1925,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(691,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(550,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1885,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(331,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Collect @ D @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_0) ).
thf(1399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Collect @ D @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(1236,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(987,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(548,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
thf(1880,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_notin__Lin__iff_1) ).
thf(1004,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) @ C ) )
| ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ C ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(298,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(1331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(485,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(1737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(363,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
thf(1463,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(611,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OatMost @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatMost__iff_0) ).
thf(2018,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_SetInterval_Oord_OatMost @ A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_lessequals @ C @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(185,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oimage @ A @ F @ D @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).
thf(1088,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oimage @ A @ F @ D @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
thf(1204,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(563,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplI_0) ).
thf(1912,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(449,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
thf(1653,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(577,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).
thf(1945,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(1009,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(533,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B )
= ( c_Collect @ ( c_COMBB @ c_Not @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B ) @ tc_bool @ tc_bool @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__eq_0) ).
thf(1848,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B )
= ( c_Collect @ ( c_COMBB @ c_Not @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B ) @ tc_bool @ tc_bool @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(629,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Set_Oimage @ B @ ( c_HOL_Ominus__class_Ominus @ D @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E @ A ) ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
thf(2059,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Set_Oimage @ B @ ( c_HOL_Ominus__class_Ominus @ D @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E @ A ) ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(565,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_Equiv__Relations_Oequiv @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).
thf(1917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Relation_OImage @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( c_Equiv__Relations_Oequiv @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(676,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(651,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).
thf(2106,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_prod @ C @ C ) ) @ ( c_Pair @ B @ D @ C @ C ) ) @ A ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(643,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(2087,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(340,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ ( tc_fun @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
thf(1417,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ ( tc_fun @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(972,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(2620,plain,
$false,
inference(e,[status(thm)],[892,1322,1718,2094,1469,1633,2072,1105,846,1031,1899,1840,1850,1982,1179,1554,1501,809,1168,760,2109,1454,666,1818,1882,1068,1618,1401,1544,1728,1269,1855,2077,1158,762,1596,1406,1443,1808,878,655,1971,1793,1041,861,1705,1655,2035,1735,1867,1872,1327,945,1063,2042,1164,1999,1919,1988,1761,1342,913,2046,1914,1391,1441,2020,885,1613,1935,1921,1359,1386,2082,1366,1967,1803,1703,1482,1254,1430,719,1313,1992,1055,724,1760,1298,1860,1264,1511,751,934,1191,1059,1132,817,853,1892,1514,2049,1398,1115,1568,1232,1319,1890,969,1347,1013,770,2024,1641,1815,1494,1362,1963,1489,924,1465,1302,1811,1373,1136,1828,1677,1960,1581,1714,2027,1858,1864,1383,1020,1183,1283,2073,981,1843,687,1928,1447,866,1394,1526,1351,660,998,1345,1600,1521,1975,1796,1072,1119,1622,774,2103,1405,1943,1201,1697,1242,849,1651,2011,1206,1691,1438,1199,1783,1311,1768,714,2061,1636,1047,798,1057,1274,1223,1091,778,952,1519,1355,1666,1487,693,729,1238,1560,1723,910,1570,1174,1751,820,1824,788,1370,2032,815,1423,1938,1968,1951,830,1210,757,1128,1281,1910,1106,1888,1296,665,2068,1624,1836,1787,1079,1027,682,1195,2112,1291,710,1573,974,2100,1270,1375,725,1425,1878,1138,869,1755,989,1592,742,697,1234,874,1143,1534,1017,1953,1111,1227,1498,1587,1096,1672,1683,1329,1160,1659,669,1424,2080,1414,1791,1214,1644,1744,1419,1739,1461,901,1075,679,1039,1825,1776,1588,1451,1668,1932,2006,1947,1984,1002,1874,1720,1979,1393,1627,1150,1478,1249,1539,1456,1266,1831,984,911,2052,1246,1333,1434,1779,921,1170,1895,1185,1996,1732,1202,792,1086,938,1563,657,765,1712,1846,1286,1035,1187,674,1663,2089,906,2001,1764,1680,1103,1219,1747,1548,745,689,1278,1906,1631,733,1154,1007,843,1620,1752,1929,2016,1701,1965,1124,1256,904,975,1615,1389,875,826,958,1403,1428,1503,936,2029,1707,1371,1258,947,1675,672,1897,804,2079,2084,1894,1349,1542,1122,1571,1307,2065,1853,1408,784,1117,1806,1011,1492,1603,1771,737,880,1043,1801,890,1471,1339,1731,1162,1862,700,915,1556,943,1061,1820,1688,858,1557,1838,1325,1029,895,1177,1381,1396,768,695,780,883,1015,1113,1000,2022,1364,1496,851,1694,983,2075,1594,1699,1066,1445,1528,1583,2096,1304,1166,1208,1467,795,663,1420,1134,1081,1990,1340,1145,754,1049,2054,722,927,2037,812,1509,1181,823,836,1551,776,1798,712,855,1961,1025,887,1566,1605,1647,739,1368,1267,1531,1098,993,1516,1598,1070,872,705,1156,1225,707,1941,1252,2092,1716,1432,1869,1901,2044,1130,1336,1813,1300,840,1785,2056,1766,703,1536,1023,1221,864,1749,727,1670,1272,1353,1955,1485,1972,1052,1506,1585,1094,978,1140,1240,991,1617,2013,1459,1949,1834,1412,1126,1108,1316,1649,1084,931,1685,1781,1216,1448,1189,2110,1575,1289,1453,963,1476,1639,1903,1101,1523,781,995,1276,1590,2098,748,1629,2004,1244,1822,731,786,2009,1294,929,1308,1193,1077,1212,1607,1309,1994,1045,716,899,1661,832,684,1908,1774,1725,967,1229,1546,1876,1986,1148,1757,1480,735,1578,1957,950,835,790,2050,1657,807,2070,1561,1789,828,2040,955,1742,1436,1859,918,801,1172,897,1410,1033,1710,1197,960,1473,2063,1610,839,1977,1261,1152,1532,1384,1378,1550,1357,908,1923,1925,691,1885,1399,1236,987,1880,1004,1331,1737,1463,2018,1037,1088,1204,1912,1653,940,1945,1009,1848,2059,1917,676,2106,2087,1417,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SCT006-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.11 % Command : run_Leo-III %s %d
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Thu May 18 15:30:35 EDT 2023
% 0.11/0.30 % CPUTime :
% 0.74/0.74 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.37/0.97 % [INFO] Parsing done (223ms).
% 1.37/0.98 % [INFO] Running in sequential loop mode.
% 2.08/1.18 % [INFO] eprover registered as external prover.
% 2.08/1.18 % [INFO] cvc4 registered as external prover.
% 2.08/1.19 % [INFO] Scanning for conjecture ...
% 2.22/1.31 % [INFO] Found a conjecture and 653 axioms. Running axiom selection ...
% 2.88/1.44 % [INFO] Axiom selection finished. Selected 653 axioms (removed 0 axioms).
% 3.83/1.62 % [INFO] Problem is propositional (TPTP CNF).
% 3.83/1.64 % [INFO] Type checking passed.
% 3.83/1.64 % [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 ...
% 15.87/4.07 % External prover 'e' found a proof!
% 15.87/4.07 % [INFO] Killing All external provers ...
% 15.87/4.07 % Time passed: 3649ms (effective reasoning time: 3095ms)
% 15.87/4.07 % 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)>
% 15.87/4.08 % Axioms used in derivation (653): cls_inf__sup__absorb_0, cls_inf__sup__aci_I2_J_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_subset__insert_1, cls_Diff__iff_2, cls_Diff1__fold__graph_0, cls_Compl__subset__Compl__iff_1, clsarity_nat__HOL_Oord, cls_vimage__code_0, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_Diff__cancel_0, cls_INT__extend__simps_I4_J_0, cls_PiE_0, cls_Int__absorb2_0, cls_minus__le__iff_0, cls_Inter__lower_0, cls_order__le__less__trans_0, cls_equiv__class__eq__iff_0, cls_sup__ge1_0, cls_image__constant_0, cls_Compl__Diff__eq_0, cls_compl__sup_0, cls_insertE_0, cls_less__fun__def_1, cls_Un__Diff_0, cls_Un__subset__iff_0, cls_ball__conj__distrib_3, cls_insert__inter__insert_0, cls_inj__on__Un_2, cls_Pi__I_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_converseI_0, cls_InterI_1, cls_equalityI_0, cls_COMBC__def_0, cls_subset__image__iff_2, cls_Image__singleton__iff_0, cls_Diff__eq_0, cls_empty__is__image_1, cls_image__mono_0, cls_Un__empty__left_0, cls_le__funD_0, cls_fun__upd__image_1, cls_xt1_I12_J_0, cls_funcsetI_0, cls_subset__empty_1, cls_Pi__mem_0, cls_funcset__image_0, cls_inj__on__image__Int_0, cls_sup__bot__right_0, cls_insert__code_1, cls_fun__upd__apply_1, clsarity_nat__Lattices_Odistrib__lattice, clsarity_bool__Lattices_Olower__semilattice, cls_le__SUPI_0, cls_linorder__neqE_0, cls_vimage__Diff_0, cls_bexCI_0, cls_Un__upper1_0, cls_UN__extend__simps_I10_J_0, cls_Un__commute_0, clsarity_fun__Orderings_Oorder, cls_UnCI_1, cls_Compl__eq_0, cls_distrib__sup__le_0, cls_Int__mono_0, cls_le__iff__inf_1, cls_complete__lattice_OSup__singleton_0, cls_CHAINED_0, cls_inf__sup__aci_I6_J_0, cls_COMBK__def_0, cls_ord_OgreaterThan__iff_0, cls_Diff__Un_0, cls_empty__iff_0, cls_le__inf__iff_1, cls_vimage__Collect__eq_0, cls_Diff__subset__conv_0, cls_mem__def_1, cls_bexE_1, cls_fun__upd__image_0, clsarity_nat__Orderings_Olinorder, cls_Int__insert__left_0, cls_ball__conj__distrib_11, cls_Int__Collect_1, cls_Inf__lower_0, cls_insert__absorb_0, cls_equiv__class__self_0, cls_Int__subset__iff_2, cls_image__vimage__subset_0, cls_inj__on__image__set__diff_0, cls_less__supI1_0, cls_minus__diff__eq_0, cls_Int__Un__distrib2_0, cls_compl__eq__compl__iff_0, cls_inf1E_1, cls_Image__Un_0, cls_Diff__triv_0, cls_minus__minus_0, cls_insert__iff_1, cls_insert__subset_0, cls_bex__UN_3, cls_sup__inf__distrib2_0, clsarity_fun__Lattices_Oupper__semilattice, cls_fold__graph_H_Ointros_I1_J_0, cls_ballE_0, cls_inj__on__Un__image__eq__iff_0, cls_less__minus__iff_0, cls_fold__graph_H_Ointros_I2_J_0, cls_setsum__diff1__nat_1, cls_inf__sup__distrib1_0, cls_order__less__trans_0, cls_neg__less__iff__less_1, cls_Int__absorb1_0, cls_le__sup__iff_0, cls_ComplD_0, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_inf__left__commute_0, cls_pred__equals__eq_0, cls_ord_OatLeastAtMost__iff_2, cls_COMBB__def_0, cls_disjoint__eq__subset__Compl_0, cls_CollectI_0, cls_inf__commute_0, cls_Collect__neg__eq_0, cls_Un__left__commute_0, cls_vimage__Compl_0, cls_subset__insert__iff_2, cls_type__definition_OAbs__inverse_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_Pi__I_H_1, cls_diff__eq_0, cls_Un__Int__distrib2_0, cls_Int__empty__right_0, cls_neg__equal__iff__equal_0, cls_extensionalityI_0, cls_Collect__empty__eq_0, cls_equiv__class__eq__iff_3, cls_UN__extend__simps_I1_J_0, cls_psubset__insert__iff_8, cls_CollectD_0, cls_not__psubset__empty_0, cls_vimage__insert_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_order__less__asym_0, cls_Union__disjoint_0, cls_linorder__not__less_0, cls_Inf__singleton_0, cls_le__supI_0, cls_inf__eq__neg__sup_0, cls_Un__subset__iff_1, cls_Inf__binary_0, cls_SUP__const_0, cls_order__le__less_0, cls_order__less__asym_H_0, cls_inj__on__Un_3, cls_rev__image__eqI_0, cls_SUP1__I_0, cls_eq__equiv__class__iff2_1, cls_UN__iff_2, cls_linorder__antisym__conv2_0, cls_le__iff__sup_0, cls_empty__is__image_0, cls_psubset__eq_1, cls_UN__extend__simps_I3_J_0, cls_order__eq__refl_0, cls_ord_OatLeastLessThan__iff_0, cls_neg__sup__eq__inf_0, cls_linorder__antisym__conv1_0, cls_ord_OgreaterThanAtMost__iff_1, cls_inj__on__insert_0, cls_Image__empty_0, cls_UN__absorb_0, clsarity_fun__Orderings_Obot, cls_le__supE_1, cls_fun__upd__other_0, cls_ball__conj__distrib_1, cls_type__definition_ORep__inject_0, cls_notin__Lin__iff_0, cls_minus__less__iff_1, cls_sup__eq__neg__inf_0, cls_Union__upper_0, cls_psubset__insert__iff_5, cls_Un__absorb2_0, cls_psubset__trans_0, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_image__constant__conv_1, cls_vimageI_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_less__le__not__le_2, cls_override__on__apply__notin_0, cls_xt1_I10_J_0, cls_le__minus__iff_0, cls_ball__conj__distrib_9, cls_sup__eq__bot__eq2_0, cls_ball__conj__distrib_4, cls_UnCI_0, cls_Int__insert__right_1, cls_Compl__disjoint2_0, cls_not__less__iff__gr__or__eq_0, cls_UN__Un_0, cls_Sup__singleton_0, cls_UN__constant_0, cls_bexCI_1, cls_Lin__irrefl_0, cls_Un__upper2_0, cls_singleton__iff_1, cls_complete__lattice_OInf__empty_0, cls_subset__iff_0, cls_insert__code_2, cls_bex__Un_6, cls_Diff__idemp_0, cls_subset__empty_0, cls_equiv__class__eq_0, cls_subset__Compl__self__eq_1, cls_UnionE_1, cls_insert__Diff__single_0, cls_bexI_1, cls_UN__simps_I10_J_0, cls_ord_OgreaterThanAtMost__iff_0, cls_Collect__mem__eq_0, clsarity_fun__HOL_Oord, cls_Compl__Un_0, cls_rev__predicate1D_0, cls_extensional__arb_0, cls_image__insert_0, cls_UN__subset__iff_0, cls_vimage__Un_0, cls_diff__single__insert_0, cls_SUP1__iff_2, cls_inf__absorb2_0, cls_ball__conj__distrib_0, clsarity_bool__Lattices_Oupper__semilattice, cls_le__minus__iff_1, cls_fold__graph_OinsertI_0, cls_ord_OlessThan__iff_0, cls_type__definition_ORep__inverse_0, cls_doubleton__eq__iff_2, cls_Compl__disjoint_0, cls_bex__UN_4, cls_ball__conj__distrib_10, cls_Sup__binary_0, cls_Int__Collect_0, cls_Un__insert__left_0, cls_inf__sup__ord_I2_J_0, cls_vimage__singleton__eq_1, cls_subset__insert__iff_3, cls_Inf__insert_0, cls_fun__upd__triv_0, clsarity_nat__Orderings_Obot, cls_xt1_I8_J_0, cls_vimage__const_1, cls_inf__sup__aci_I3_J_0, cls_Un__mono_0, cls_less__infI1_0, cls_Int__insert__left_1, cls_insert__subset_1, cls_Int__empty__left_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_Image__singleton__iff_1, cls_psubset__insert__iff_4, cls_bex__Un_5, cls_PowI_0, clsarity_nat__Lattices_Olower__semilattice, cls_Pow__top_0, cls_ex__in__conv_0, cls_sup__commute_0, cls_Compl__anti__mono_0, cls_Image__subset__eq_1, cls_set__eq__subset_2, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_subset__iff__psubset__eq_0, cls_neg__inf__eq__sup_0, cls_compl__inf__bot_0, cls_not__leE_0, cls_Un__subset__iff_2, cls_fold__graph_OemptyI_0, cls_linorder__linear_0, cls_Un__empty_0, cls_bex__Un_7, clsarity_fun__Lattices_Olattice, cls_Int__assoc_0, cls_extensionalityI_1, cls_order__antisym_0, cls_order__trans_0, cls_bexE_0, cls_psubset__insert__iff_9, cls_subset__trans_0, cls_double__diff_0, cls_inf__le2_0, cls_Compl__eq__Compl__iff_0, cls_insert__is__Un_0, cls_ord_OatLeastAtMost__iff_1, cls_ord_OgreaterThanLessThan__iff_0, cls_image__empty_0, cls_Compl__subset__Compl__iff_0, cls_insertI1_0, cls_DiffI_0, cls_eq__equiv__class__iff2_0, cls_psubset__insert__iff_6, cls_ord_OgreaterThanAtMost__iff_2, cls_Image__iff_2, cls_le__supE_0, cls_subset__Compl__self__eq_0, cls_empty__not__insert_0, cls_inf__compl__bot_0, cls_sup__assoc_0, cls_Diff__Int__distrib2_0, cls_image__constant__conv_0, cls_linorder__antisym__conv1_1, cls_inj__on__insert_1, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_Un__Int__crazy_0, clsarity_bool__Orderings_Opreorder, cls_singleton__conv_0, cls_insert__Diff1_0, cls_Image__Int__subset_0, cls_empty__subsetI_0, cls_fun__upd__twist_0, cls_linorder__not__le_1, cls_ord_OatLeastLessThan__iff_1, cls_Un__absorb1_0, cls_type__definition_ORep_0, cls_Diff__insert2_0, cls_Int__commute_0, cls_Sup__upper_0, cls_sup__least_0, cls_ball__conj__distrib_8, cls_rev__ImageI_0, cls_Pair__eq_0, cls_doubleton__eq__iff_0, cls_inf__sup__aci_I1_J_0, cls_override__on__apply__in_0, cls_sup1E_0, cls_distrib__inf__le_0, cls_converse__iff_1, cls_minus__less__iff_0, cls_subset__refl_0, cls_converse__in__Lin_0, cls_singletonE_0, cls_image__diff__subset_0, cls_Pow__bottom_0, clsarity_nat__Lattices_Olattice, cls_inj__on__empty_0, cls_DiffE_0, cls_Int__Diff_0, cls_image__iff_2, cls_less__minus__iff_1, cls_insertCI_0, cls_psubset__eq_0, cls_image__Int__subset_0, cls_ball__conj__distrib_5, cls_le__inf__iff_2, cls_pred__subset__eq_1, cls_Un__Diff__cancel_0, cls_inj__on__iff_0, clsarity_nat__Orderings_Opreorder, cls_complete__lattice_OInf__insert_0, cls_image__Un_0, cls_insert__Diff_0, cls_not__less__iff__gr__or__eq_1, cls_ord_OlessThan__iff_1, cls_equation__minus__iff_0, cls_sup1CI_1, cls_complete__lattice_OInf__binary_0, cls_order__le__neq__trans_0, cls_le__infE_0, cls_UnionE_0, cls_SUP2__iff_2, cls_fun__upd__apply_0, cls_complete__lattice_OSup__binary_0, clsarity_fun__Lattices_Oboolean__algebra, cls_subset__equiv__class_0, cls_vimage__Int_0, cls_order__eq__iff_2, cls_le__infI1_0, cls_Int__absorb_0, cls_inf__assoc_0, cls_linorder__neqE__ordered__idom_0, cls_insert__mono_0, cls_le__supI2_0, cls_less__le__not__le_1, cls_Un__assoc_0, cls_Un__Diff__cancel2_0, cls_Collect__def_0, cls_bot1E_0, cls_linorder__antisym__conv3_0, cls_Int__lower2_0, cls_UN__constant_1, cls_bexI_0, cls_bex__empty_0, cls_PowD_0, cls_Pi__I_1, cls_Diff__disjoint_0, cls_inf__sup__ord_I4_J_0, cls_psubset__insert__iff_0, cls_Diff__Int__distrib_0, cls_psubset__insert__iff_1, cls_UnE_0, cls_inj__on__Un_0, cls_subset__insertI2_0, cls_vimage__mono_0, cls_Int__left__absorb_0, cls_order__neq__le__trans_0, cls_doubleton__eq__iff_3, cls_Compl__Int_0, cls_converseD_0, cls_inj__on__fun__updI_0, cls_complete__lattice_Odual__complete__lattice_0, cls_Diff__mono_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_psubset__subset__trans_0, cls_inj__on__def_0, cls_Un__absorb_0, cls_order__antisym__conv_0, cls_psubsetD_0, cls_ord_OatLeastAtMost__iff_0, cls_SUP2__I_0, cls_Int__lower1_0, cls_InterD_0, clsarity_bool__Lattices_Olattice, cls_psubset__insert__iff_3, cls_Union__quotient_0, cls_eq__eqI_0, cls_vimage__eq_1, cls_bexCI_3, cls_order__less__le_2, cls_Un__Int__distrib_0, clsarity_bool__Lattices_Obounded__lattice, cls_inf__sup__ord_I1_J_0, cls_le__infI_0, cls_le__imp__neg__le_0, cls_override__on__emptyset_0, cls_subset__insert__iff_4, cls_Int__subset__iff_0, cls_linorder__less__linear_0, cls_type__definition_OAbs__inject_0, cls_insert__subset_2, cls_le__supI1_0, cls_le__eqI_0, cls_sup__left__idem_0, cls_complete__lattice_OSup__insert_0, cls_subsetD_0, cls_rev__bexI_0, cls_xt1_I11_J_0, cls_inf__idem_0, clsarity_fun__Complete__Lattice_Ocomplete__lattice, cls_quotientE_0, cls_complete__lattice_OInf__lower_0, cls_bspec_1, cls_vimageE_0, cls_inf__bot__left_0, cls_inf1I_0, cls_Union__Pow__eq_0, cls_insert__not__empty_0, cls_Int__left__commute_0, cls_le__sup__iff_2, clsarity_fun__Lattices_Obounded__lattice, cls_equiv__class__subset_0, cls_insert__absorb2_0, cls_Image__subset__eq_0, cls_UNION__empty__conv_I1_J_0, cls_fun__upd__idem_0, cls_inf__sup__aci_I4_J_0, cls_sup__inf__absorb_0, cls_double__compl_0, cls_subset__singletonD_0, cls_Int__iff_2, cls_notin__Lin__iff_1, cls_Un__Int__assoc__eq_1, cls_doubleton__eq__iff_1, cls_UN__extend__simps_I2_J_0, cls_eq__equiv__class__iff_0, cls_fun__upd__idem__iff_0, cls_Sup__insert_0, cls_vimage__singleton__eq_0, cls_xt1_I6_J_0, cls_subset__insert__iff_0, cls_vimage__code_1, cls_UN__I_0, cls_ComplI_0, cls_converse__converse_0, cls_ord_OgreaterThanLessThan__iff_1, cls_quotient__disj_0, cls_equiv__class__eq__iff_1, cls_subset__psubset__trans_0, clsarity_bool__Complete__Lattice_Ocomplete__lattice, cls_Diff__empty_0, cls_empty__Collect__eq_0, cls_IntI_0, cls_eq__equiv__class_0, cls_minus__le__iff_1, cls_complete__lattice_OInf__singleton_0, cls_inf__greatest_0, cls_Sup__empty_0, cls_Un__left__absorb_0, cls_linorder__not__le_0, cls_order__less__irrefl_0, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_inf__sup__aci_I5_J_0, cls_Diff__Int_0, cls_less__supI2_0, cls_neg__le__iff__le_0, cls_ord_OatLeastLessThan__iff_2, cls_less__fun__def_2, cls_Un__empty_1, cls_le__iff__inf_0, clsarity_bool__Lattices_Oboolean__algebra, cls_subset__insert_0, cls_sup__idem_0, clsarity_nat__Lattices_Oupper__semilattice, cls_InterI_0, cls_emptyE_0, cls_inf__sup__ord_I3_J_0, cls_fun__upd__same_0, cls_less__infI2_0, cls_ball__conj__distrib_7, cls_funcset__mem_0, cls_ball__conj__distrib_6, cls_eq__eqI_1, cls_Diff__Compl_0, cls_insert__def_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_subset__inj__on_0, cls_singleton__inject_0, cls_bex__Un_4, cls_less__eqI_0, cls_vimageI2_0, cls_sup__ge2_0, clsarity_fun__Orderings_Opreorder, cls_converse__in__Lin_1, cls_UN__upper_0, cls_IntE_1, cls_IntE_0, cls_Un__least_0, cls_double__complement_0, cls_inj__on__contraD_0, cls_Int__greatest_0, cls_equation__minus__iff_1, cls_sup1CI_0, cls_inj__onD_0, cls_Union__disjoint_2, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_le__infE_1, cls_image__eqI_0, cls_pred__subset__eq_0, cls_image__subset__iff_0, cls_inf__le1_0, cls_insertCI_1, cls_inf__left__idem_0, cls_complete__lattice_OSup__upper_0, cls_compl__inf_0, cls_empty__fold__graphE_0, clsarity_bool__Lattices_Odistrib__lattice, cls_inj__on__diff_0, cls_inj__on__insert_2, cls_funcsetI_1, cls_setsum__negf_0, cls_doubleton__eq__iff_4, cls_ord_OatMost__iff_0, cls_UnionI_0, cls_Diff__subset__conv_1, cls_rev__bexI_1, cls_insert__code_0, cls_le__eqI_1, cls_vimageD_0, cls_Diff__Int2_0, cls_quotient__eqI_0, cls_vimage__def_0, cls_complete__lattice_OSup__empty_0, cls_Un__Diff__Int_0, cls_subset__insertI_0, cls_ord_OgreaterThanLessThan__iff_2, cls_bexCI_2, cls_order__less__imp__le_0, cls_minus__equation__iff_1, cls_DiffE_1, cls_equiv__class__nondisjoint_0, cls_Diff__partition_0, cls_insert__image_0, cls_fun__upd__upd_0, cls_psubset__insert__iff_2, cls_disjoint__iff__not__equal_0, cls_ord_OatMost__iff_1, cls_inj__on__Un_1, cls_sup__inf__distrib1_0, cls_vimage__empty_0, cls_Un__Int__assoc__eq_0, cls_insert__commute_0, cls_quotientI_0, cls_insert__iff_2, cls_image__image_0, cls_Diff__insert__absorb_0, cls_le__infI2_0, cls_UNION__empty__conv_I2_J_0, cls_sup__bot__left_0, cls_ord_OgreaterThan__iff_1, clsarity_nat__Orderings_Oorder, cls_xt1_I7_J_0, cls_image__is__empty_0, cls_imageI_0, clsarity_fun__Lattices_Odistrib__lattice, cls_disjoint__eq__subset__Compl_1, cls_less__eqI_1, cls_order__less__le_1, cls_less__fun__def_0, cls_equiv__class__eq__iff_2, cls_linorder__not__less_1, cls_UN__insert_0, cls_quotient__eq__iff_0, cls_Un__insert__right_0, cls_ballE_1, cls_psubset__insert__iff_7, cls_Pair__eq_1, cls_quotientE_1, cls_equalityE_0, cls_Pi__I_H_0, cls_inf__sup__distrib2_0, cls_inf__bot__right_0, cls_sup__absorb1_0, cls_neg__less__iff__less_0, cls_Union__disjoint_1, cls_ball__empty_0, cls_Int__insert__right_0, cls_singleton__conv2_0, cls_UN__empty2_0, cls_psubset__eq_2, cls_bspec_0, cls_subset__insert__iff_1, cls_eq__equiv__class__iff_1, cls_ball__conj__distrib_2, cls_Diff__subset_0, cls_predicate1D_0, cls_inf1E_0, cls_empty__Diff_0, cls_Int__Collect_2, cls_fun__upd__idem__iff_1
% 15.87/4.08 % No. of inferences in proof: 1309
% 15.87/4.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3649 ms resp. 3095 ms w/o parsing
% 16.80/4.31 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.80/4.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------