TSTP Solution File: SCT077-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT077-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 11:50:25 EDT 2023
% Result : Unsatisfiable 51.46s 12.08s
% Output : Refutation 52.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 793
% Syntax : Number of formulae : 1482 ( 405 unt; 105 typ; 0 def)
% Number of atoms : 2863 ( 838 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 32132 (1396 ~;1486 |; 0 &;29250 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 155 ( 155 >; 0 *; 0 +; 0 <<)
% Number of symbols : 107 ( 105 usr; 22 con; 0-9 aty)
% Number of variables : 4940 ( 0 ^;4940 !; 0 ?;4940 :)
% 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_Arrow__Order__Mirabelle_Oindi_type,type,
tc_Arrow__Order__Mirabelle_Oindi: $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_COMBC_type,type,
c_COMBC: $i > $i > $i > $i ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i ).
thf(c_HOL_OIf_type,type,
c_HOL_OIf: $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i ).
thf(v_h_____type,type,
v_h____: $i ).
thf(v_n_type,type,
v_n: $i ).
thf(v_Lab_____type,type,
v_Lab____: $i ).
thf(v_Lba_____type,type,
v_Lba____: $i ).
thf(c_Collect_type,type,
c_Collect: $i > $i ).
thf(c_All_type,type,
c_All: $i > $i ).
thf(c_COMBS_type,type,
c_COMBS: $i > $i > $i > $i ).
thf(c_implies_type,type,
c_implies: $i ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(c_Arrow__Order__Mirabelle_OLin_type,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(c_Fun_Oinj__on_type,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_COMBI_type,type,
c_COMBI: $i > $i ).
thf(class_Finite__Set_Ofinite_Ofinite_type,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
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_lessequals_type,type,
c_lessequals: $i > $i ).
thf(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
thf(c_FuncSet_OPi_type,type,
c_FuncSet_OPi: $i > $i > $i > $i > $i ).
thf(class_Lattices_Obounded__lattice_type,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(t_a_type,type,
t_a: $i ).
thf(v_x_type,type,
v_x: $i ).
thf(class_Lattices_Olower__semilattice_type,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(class_Lattices_Oupper__semilattice_type,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
thf(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1_type,type,
v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1: $i ).
thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
thf(c_Lattices_Oboolean__algebra_type,type,
c_Lattices_Oboolean__algebra: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OINFI_type,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_Finite__Set_Osetsum_type,type,
c_Finite__Set_Osetsum: $i > $i > $i ).
thf(c_and_type,type,
c_and: $i ).
thf(c_fequal_type,type,
c_fequal: $i > $i ).
thf(c_or_type,type,
c_or: $i ).
thf(class_Orderings_Otop_type,type,
class_Orderings_Otop: $i > $o ).
thf(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_type,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_Set_Ovimage_type,type,
c_Set_Ovimage: $i > $i > $i > $i ).
thf(c_Predicate_OPowp_type,type,
c_Predicate_OPowp: $i > $i > $i > $i ).
thf(v_B_type,type,
v_B: $i ).
thf(class_Ring__and__Field_Oring_type,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(class_Complete__Lattice_Ocomplete__lattice_type,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_Complete__Lattice_OSup__class_OSup_type,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i ).
thf(c_Complete__Lattice_OInf__class_OInf_type,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_type,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(c_Arrow__Order__Mirabelle_Obelow_type,type,
c_Arrow__Order__Mirabelle_Obelow: $i > $i > $i > $i ).
thf(c_Not_type,type,
c_Not: $i ).
thf(v_f_type,type,
v_f: $i ).
thf(t_b_type,type,
t_b: $i ).
thf(v_A_type,type,
v_A: $i ).
thf(c_Ex_type,type,
c_Ex: $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(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1: $i > $i > $i > $i > $i ).
thf(class_HOL_Oord_type,type,
class_HOL_Oord: $i > $o ).
thf(c_Hilbert__Choice_OLeastM_type,type,
c_Hilbert__Choice_OLeastM: $i > $i > $i > $i > $i ).
thf(c_Hilbert__Choice_OEps_type,type,
c_Hilbert__Choice_OEps: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1_type,type,
c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1: $i > $i ).
thf(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(class_Ring__and__Field_Oordered__ring__strict_type,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(c_Inductive_Ocomplete__lattice_Ogfp_type,type,
c_Inductive_Ocomplete__lattice_Ogfp: $i > $i > $i > $i ).
thf(class_Lattices_Odistrib__lattice_type,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(class_Ring__and__Field_Osemiring__0_type,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(class_Lattices_Oboolean__algebra_type,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(class_HOL_Ouminus_type,type,
class_HOL_Ouminus: $i > $o ).
thf(c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2_type,type,
c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2: $i > $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__add_type,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(c_Inductive_Ocomplete__lattice_Olfp_type,type,
c_Inductive_Ocomplete__lattice_Olfp: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2_type,type,
c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2: $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Oabove_type,type,
c_Arrow__Order__Mirabelle_Oabove: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omktop_type,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1_type,type,
c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1: $i > $i > $i ).
thf(v_a_type,type,
v_a: $i ).
thf(c_Arrow__Order__Mirabelle_Omkbot_type,type,
c_Arrow__Order__Mirabelle_Omkbot: $i > $i > $i ).
thf(c_Hilbert__Choice_OGreatestM_type,type,
c_Hilbert__Choice_OGreatestM: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1_type,type,
c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1_type,type,
c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1: $i > $i > $i ).
thf(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1_type,type,
v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1: $i > $i > $i ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(530,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(1879,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(1024,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
thf(1369,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(613,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__INT__distrib_0) ).
thf(2072,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(578,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(1995,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(464,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(1729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(512,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
thf(1840,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
thf(1315,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_1) ).
thf(1950,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(446,axiom,
( ( c_FuncSet_OPi @ v_A @ v_B @ t_a @ t_b )
= ( hAPP @ ( c_Collect @ ( tc_fun @ t_a @ t_b ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ ( tc_fun @ t_a @ t_b ) ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ t_b ) ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ t_b @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_a @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( tc_fun @ t_a @ t_b ) ) @ ( c_COMBS @ t_a @ ( tc_fun @ t_b @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBB @ t_b @ ( tc_fun @ ( tc_fun @ t_b @ tc_bool ) @ tc_bool ) @ t_a ) @ ( c_in @ t_b ) ) ) ) @ v_B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__def__raw_0) ).
thf(1686,plain,
( ( c_FuncSet_OPi @ v_A @ v_B @ t_a @ t_b )
= ( hAPP @ ( c_Collect @ ( tc_fun @ t_a @ t_b ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ ( tc_fun @ t_a @ t_b ) ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ t_b ) ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ ( tc_fun @ t_b @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ t_a @ ( tc_fun @ t_b @ tc_bool ) ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( tc_fun @ t_a @ t_b ) ) @ ( c_COMBS @ t_a @ ( tc_fun @ t_b @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBB @ t_b @ ( tc_fun @ ( tc_fun @ t_b @ tc_bool ) @ tc_bool ) @ t_a ) @ ( c_in @ t_b ) ) ) ) @ v_B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(653,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
thf(2163,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(892,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(670,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(2199,plain,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(285,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UN__distrib_0) ).
thf(1322,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(1665,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(403,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(1586,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(364,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/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(1501,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)],[364]) ).
thf(53,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_Complete__Lattice_Ocomplete__lattice @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_lessequals @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_HOL_Oord__class_Oless @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dual__complete__lattice_0) ).
thf(809,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_Complete__Lattice_Ocomplete__lattice @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_lessequals @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_HOL_Oord__class_Oless @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(215,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
thf(1168,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(33,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ E @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ A @ E ) @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ ( c_Collect @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ D ) ) ) ) @ ( hAPP @ ( c_COMBC @ B @ E @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ tc_bool ) @ B ) @ ( c_fequal @ E ) ) @ F ) ) ) ) ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ B @ E ) @ D ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__image__gen_0) ).
thf(760,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ E @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ A @ E ) @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ ( c_Collect @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ D ) ) ) ) @ ( hAPP @ ( c_COMBC @ B @ E @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ E @ ( tc_fun @ E @ tc_bool ) @ B ) @ ( c_fequal @ E ) ) @ F ) ) ) ) ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ B @ E ) @ D ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(632,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ B ) )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ C @ F @ G @ H @ A @ I @ D @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Osup__compl__top_0) ).
thf(2109,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ B ) )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ C @ F @ G @ H @ A @ I @ D @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(640,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(2131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(594,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
thf(2031,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(392,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ F ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
thf(1559,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ F ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(1105,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(503,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/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
thf(1818,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)],[503]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
thf(1295,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(143,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ A @ B ) @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ A ) @ C )
| ~ ( c_Finite__Set_Ofinite @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UN_0) ).
thf(1005,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ A @ B ) @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ A ) @ C )
| ~ ( c_Finite__Set_Ofinite @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(608,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ A @ C @ C ) @ B ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
thf(2062,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_Set_Oimage @ A @ C @ C ) @ B ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
thf(1443,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(174,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Inductive_Ocomplete__lattice_Ogfp @ A @ B @ C )
= ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ C @ ( tc_fun @ C @ C ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ C ) ) @ ( c_Collect @ C ) ) @ ( hAPP @ ( c_COMBS @ C @ C @ tc_bool ) @ B ) ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ B @ E @ F @ G @ H @ I @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Ogfp__def__raw_0) ).
thf(1073,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Inductive_Ocomplete__lattice_Ogfp @ A @ B @ C )
= ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ C @ ( tc_fun @ C @ C ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ C ) ) @ ( c_Collect @ C ) ) @ ( hAPP @ ( c_COMBS @ C @ C @ tc_bool ) @ B ) ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ B @ E @ F @ G @ H @ I @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1544,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(204,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(1142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(334,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(1437,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(519,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_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1855,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_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(229,axiom,
! [A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).
thf(1200,plain,
! [A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(615,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/sandbox/benchmark/theBenchmark.p',cls_converse__in__Lin_0) ).
thf(2077,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)],[615]) ).
thf(408,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ A ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ C @ A ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ B ) @ ( c_Collect @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBS @ C @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ C ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ ( c_in @ C ) ) @ E ) ) ) ) @ F ) ) ) ) @ G )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) @ ( c_Finite__Set_Osetsum @ B @ A ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ ( c_Collect @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ G ) ) ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ tc_bool ) @ F ) ) ) ) ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ C )
| ~ ( c_Finite__Set_Ofinite @ G @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__setsum__restrict_0) ).
thf(1596,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ A ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ C @ A ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ B ) @ ( c_Collect @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBS @ C @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ C ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ ( c_in @ C ) ) @ E ) ) ) ) @ F ) ) ) ) @ G )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ C @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) @ ( c_Finite__Set_Osetsum @ B @ A ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ A ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ ( c_Collect @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ G ) ) ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ tc_bool ) @ F ) ) ) ) ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ E @ C )
| ~ ( c_Finite__Set_Ofinite @ G @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(321,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).
thf(1406,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(629,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(2104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
thf(730,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(271,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ D ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(1290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ D ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ B ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ B ) ) @ ( hAPP @ ( c_Collect @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__disj__eq_0) ).
thf(1422,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ B ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ B ) ) @ ( hAPP @ ( c_Collect @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(396,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ E ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
thf(1569,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ E ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(625,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(2099,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(405,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ D @ ( hAPP @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
thf(1591,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ D @ ( hAPP @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(568,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(1971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(491,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ C ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
thf(1793,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ C ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(379,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(1533,plain,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(160,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ B @ tc_bool ) @ A ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ A @ D ) @ C ) ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I10_J_0) ).
thf(1041,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ B @ tc_bool ) @ A ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ A @ D ) @ C ) ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(78,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(861,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(489,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(1788,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(433,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) ) @ E ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__left__distrib_0) ).
thf(1655,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) ) @ E ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(280,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/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(1310,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)],[280]) ).
thf(467,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_1) ).
thf(1735,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(715,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(1275,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(527,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(1872,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(245,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).
thf(1233,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).
thf(698,plain,
! [A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(575,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(1988,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(477,axiom,
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ t_b )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ t_a @ t_b ) @ v_A ) @ v_f )
= ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ t_b ) @ ( hAPP @ ( c_Set_Oimage @ v_f @ t_a @ t_b ) @ v_A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INFI__def__raw_0) ).
thf(1761,plain,
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ t_b )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ t_a @ t_b ) @ v_A ) @ v_f )
= ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ t_b ) @ ( hAPP @ ( c_Set_Oimage @ v_f @ t_a @ t_b ) @ v_A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(561,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1954,plain,
class_HOL_Oord @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(599,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/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(2042,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)],[599]) ).
thf(646,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ ( c_Set_Ovimage @ A @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq__UN_0) ).
thf(2146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ ( c_Set_Ovimage @ A @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Set_Oinsert @ C ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
thf(1222,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(668,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(2195,plain,
class_HOL_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(455,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(1705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(580,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(1999,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(797,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)],[48]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(898,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(677,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__binary_0) ).
thf(2216,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(141,axiom,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(1001,plain,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(601,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ D ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__D_0) ).
thf(2046,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ D ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(399,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ B ) )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ C @ F @ G @ A @ H @ D @ I @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Oinf__compl__bot_0) ).
thf(1576,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ B ) )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ C @ F @ G @ A @ H @ D @ I @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(336,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/sandbox/benchmark/theBenchmark.p',cls_converse__in__Lin_1) ).
thf(1441,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)],[336]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( C
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
thf(973,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( C
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(553,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
thf(1935,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(617,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( C = D )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(2082,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( C = D )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(352,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ A ) @ E ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(1475,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ A ) @ E ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(302,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(611,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/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).
thf(2067,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)],[611]) ).
thf(495,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(1803,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
thf(1482,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
thf(829,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(183,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(1095,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(249,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1243,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(1127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(485,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(1782,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(589,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(2020,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_0) ).
thf(841,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(431,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(1650,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(429,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1645,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(642,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ B ) ) @ C ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__disjI_0) ).
thf(2136,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ B ) ) @ C ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(540,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(1904,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(260,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(1265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(454,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ E @ A ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1703,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ E @ A ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(270,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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
thf(1287,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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(435,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( c_COMBI @ A ) @ A @ A ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__ident_0) ).
thf(1660,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( c_COMBI @ A ) @ A @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(43,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 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(785,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 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(541,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(1907,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(521,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(1860,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(66,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(838,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(638,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ C @ ( hAPP @ ( c_Collect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ B ) ) ) ) @ E ) ) ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ C @ E @ F @ G @ H @ I @ J @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__Sup_0) ).
thf(2126,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ C @ ( hAPP @ ( c_Collect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ B ) ) ) ) @ E ) ) ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ C @ E @ F @ G @ H @ I @ J @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(117,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 ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) )
| ~ ( c_Fun_Oinj__on @ E @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
thf(949,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 ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) )
| ~ ( c_Fun_Oinj__on @ E @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(724,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Int_0) ).
thf(1055,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(322,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(1409,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__upper_0) ).
thf(917,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(702,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(751,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(281,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionI_0) ).
thf(1313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) )
| ~ ( 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)],[281]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(1279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(663,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ D ) @ ( c_Set_Oimage @ A @ B @ C ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__UN_0) ).
thf(2185,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ D ) @ ( c_Set_Oimage @ A @ B @ C ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(1455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(1059,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(200,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ B ) @ C )
= C )
| ~ ( c_Fun_Oinj__on @ A @ C @ B @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ B ) @ C ) ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).
thf(1132,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ B ) @ C )
= C )
| ~ ( c_Fun_Oinj__on @ A @ C @ B @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ B ) @ C ) ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(494,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).
thf(1800,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(73,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_Lab____ ) @ c_Arrow__Order__Mirabelle_OLin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(853,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_Lab____ ) @ c_Arrow__Order__Mirabelle_OLin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(354,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1 @ A @ C ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__UNIV_0) ).
thf(1479,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1 @ A @ C ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(192,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(1115,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(551,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ D ) ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ D ) ) ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__Compl__subset_0) ).
thf(1931,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ D ) ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ D ) ) ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(651,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
thf(2158,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(427,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ F @ tc_bool ) ) @ C ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__E_0) ).
thf(1641,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ F @ tc_bool ) ) @ C ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(361,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1494,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(565,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(1963,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(528,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ D ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I2_J_0) ).
thf(1875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ D ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(656,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(2169,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(371,axiom,
( ( c_Predicate_OPowp @ v_A @ v_B @ t_a )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_B ) ) ) @ v_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Powp__def__raw_0) ).
thf(1514,plain,
( ( c_Predicate_OPowp @ v_A @ v_B @ t_a )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_B ) ) ) @ v_A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1319,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(870,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
thf(1013,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(37,axiom,
! [A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
thf(770,plain,
! [A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(317,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I9_J_0) ).
thf(1398,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(87,axiom,
! [A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).
thf(881,plain,
! [A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(584,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(2007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(660,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(2178,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(107,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(924,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(348,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(1465,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(620,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ D ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
thf(2090,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ D ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(685,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(2236,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(1334,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(834,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(523,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ E @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert_0) ).
thf(1864,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ E @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(571,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
thf(1978,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2 @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UNIV_2) ).
thf(1383,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2 @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(442,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(1677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(268,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(1283,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
thf(821,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(905,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(1489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(325,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(1415,plain,
class_Orderings_Obot @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(276,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__INT__eq_0) ).
thf(1302,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(31,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ D ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__subset__iff_0) ).
thf(756,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ D ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(499,axiom,
class_HOL_Ouminus @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).
thf(1811,plain,
class_HOL_Ouminus @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(341,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
thf(1450,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(1109,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)],[190]) ).
thf(423,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/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
thf(1632,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)],[423]) ).
thf(564,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
thf(1960,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
thf(806,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(401,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(1581,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(125,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ E ) @ B ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(966,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ E ) @ B ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(514,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(1843,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(236,axiom,
class_Lattices_Odistrib__lattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(1215,plain,
class_Lattices_Odistrib__lattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(80,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).
thf(866,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(315,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
thf(1394,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(376,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(1526,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(687,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
thf(2242,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(320,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(1405,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(849,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(374,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ A @ B ) ) @ 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/sandbox/benchmark/theBenchmark.p',cls_mkbot__Lin_0) ).
thf(1521,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ A @ B ) ) @ 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)],[374]) ).
thf(570,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).
thf(1975,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(85,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ B ) @ F ) )
= ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ C @ E ) @ A ) @ D ) @ E @ C ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(877,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( c_Set_Oimage @ D @ E @ B ) @ F ) )
= ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ C @ E ) @ A ) @ D ) @ E @ C ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
thf(692,plain,
! [B: $i,A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(339,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 ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_bool ) ) @ E ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__iff_0) ).
thf(1447,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 ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_bool ) ) @ E ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(956,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D )
= ( hAPP @ ( c_Collect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ B ) @ ( c_in @ C ) ) @ A ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__def_0) ).
thf(1119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D )
= ( hAPP @ ( c_Collect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ B ) @ ( c_in @ C ) ) @ A ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(418,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).
thf(1622,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(411,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ouminus @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ t_a @ A ) ) @ B ) @ v_x )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ B @ v_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).
thf(1604,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ouminus @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ t_a @ A ) ) @ B ) @ v_x )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ B @ v_x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__compr_0) ).
thf(942,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(448,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(1691,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)],[448]) ).
thf(335,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_1) ).
thf(1438,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
thf(793,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)],[46]) ).
thf(278,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
thf(1306,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(208,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(1153,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(635,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(2118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(486,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(1783,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(1470,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(622,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(2093,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(480,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(1768,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(525,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(1868,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Collect @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectI_0) ).
thf(1057,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Collect @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).
thf(1163,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(93,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I5_J_0) ).
thf(894,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(952,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)],[119]) ).
thf(373,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__Int__eq_0) ).
thf(1519,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(298,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__absorb_0) ).
thf(1355,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ B ) ) @ C ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__conjI_1) ).
thf(1255,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ B ) ) @ C ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(1487,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(56,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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
thf(815,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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(532,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ C ) ) @ D )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I1_J_0) ).
thf(1883,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ C ) ) @ D )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(312,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(1387,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(462,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(1723,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(151,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I1_J_0) ).
thf(1021,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(778,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(218,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).
thf(1174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(641,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/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
thf(2133,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)],[641]) ).
thf(365,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__UN_0) ).
thf(1502,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(473,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(1751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(58,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(820,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ D ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(788,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ D ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(648,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(2150,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1238,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(587,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).
thf(2015,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(410,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(1602,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(546,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ A ) ) @ B ) @ C ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ B @ v_x ) ) @ ( hAPP @ C @ v_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(1920,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ A ) ) @ B ) @ C ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ B @ v_x ) ) @ ( hAPP @ C @ v_x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(86,axiom,
( ( hAPP @ ( c_Set_Oimage @ v_f @ t_a @ t_b ) @ v_A )
= ( hAPP @ ( c_Collect @ t_b ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_b ) @ ( c_Ex @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_b ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_b @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_b ) @ ( c_COMBB @ t_b @ tc_bool @ t_a ) ) @ ( c_fequal @ t_b ) ) ) @ v_f ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__def__raw_0) ).
thf(879,plain,
( ( hAPP @ ( c_Set_Oimage @ v_f @ t_a @ t_b ) @ v_A )
= ( hAPP @ ( c_Collect @ t_b ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ t_b ) @ ( c_Ex @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ t_b ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_b @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_b @ tc_bool ) @ ( tc_fun @ ( tc_fun @ t_a @ t_b ) @ ( tc_fun @ t_a @ tc_bool ) ) @ t_b ) @ ( c_COMBB @ t_b @ tc_bool @ t_a ) ) @ ( c_fequal @ t_b ) ) ) @ v_f ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(390,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/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1555,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)],[390]) ).
thf(220,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( B = E )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1178,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( B = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(534,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(1888,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(1457,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(419,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ D @ E ) @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__INT_0) ).
thf(1624,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ D @ E ) @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(671,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Ovimage @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ ( tc_fun @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ B @ ( tc_fun @ B @ B ) ) @ A ) @ ( c_HOL_OIf @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) @ D ) ) @ E ) @ A @ B ) @ F )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ F ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__if_3) ).
thf(2200,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Ovimage @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ ( tc_fun @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ B @ ( tc_fun @ B @ B ) ) @ A ) @ ( c_HOL_OIf @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) @ D ) ) @ E ) @ A @ B ) @ F )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ F ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(211,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(1159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(233,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) )
| ~ ( c_Fun_Oinj__on @ E @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
thf(1210,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) )
| ~ ( c_Fun_Oinj__on @ E @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(1079,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(267,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(1281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(398,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__insert__distrib_0) ).
thf(1573,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(554,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__def_0) ).
thf(1938,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).
thf(847,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(510,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1 @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UNIV_0) ).
thf(1836,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1 @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(661,axiom,
! [A: $i] :
( ( c_FuncSet_Oextensional @ v_A @ t_a @ A )
= ( hAPP @ ( c_Collect @ ( tc_fun @ t_a @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ ( tc_fun @ t_a @ A ) ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ A ) ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ t_a ) @ c_Not ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ t_a @ A ) @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( tc_fun @ t_a @ A ) ) @ ( c_COMBC @ t_a @ A @ tc_bool ) ) @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_bool ) @ t_a ) @ ( c_fequal @ A ) ) ) ) @ ( c_HOL_Oundefined @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_extensional__def__raw_0) ).
thf(2181,plain,
! [A: $i] :
( ( c_FuncSet_Oextensional @ v_A @ t_a @ A )
= ( hAPP @ ( c_Collect @ ( tc_fun @ t_a @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool @ ( tc_fun @ t_a @ A ) ) @ ( c_All @ t_a ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ A ) ) @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ t_a ) @ c_Not ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ t_a @ A ) @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( tc_fun @ t_a @ A ) ) @ ( c_COMBC @ t_a @ A @ tc_bool ) ) @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_bool ) @ t_a ) @ ( c_fequal @ A ) ) ) ) @ ( c_HOL_Oundefined @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(227,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(1195,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(675,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
thf(2211,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(314,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I9_J_0) ).
thf(1392,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(682,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ A ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ B @ tc_bool ) @ D ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I10_J_0) ).
thf(2228,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ A ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ B @ tc_bool ) @ D ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(633,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__disjoint_0) ).
thf(2112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_FuncSet_OPi @ A @ B @ C @ D )
= ( hAPP @ ( c_Collect @ ( tc_fun @ C @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ tc_bool @ ( tc_fun @ C @ D ) ) @ ( c_All @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ D ) ) @ ( hAPP @ ( c_COMBS @ C @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ C ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ ( c_in @ C ) ) @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ ( tc_fun @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ D ) ) @ ( c_COMBS @ C @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ C ) @ ( c_in @ D ) ) ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__def_0) ).
thf(710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_FuncSet_OPi @ A @ B @ C @ D )
= ( hAPP @ ( c_Collect @ ( tc_fun @ C @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ tc_bool @ ( tc_fun @ C @ D ) ) @ ( c_All @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ D ) ) @ ( hAPP @ ( c_COMBS @ C @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ C ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ C @ tc_bool ) @ tc_bool ) @ ( c_in @ C ) ) @ A ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ D ) @ ( tc_fun @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ D ) ) @ ( c_COMBS @ C @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ C ) @ ( c_in @ D ) ) ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(469,axiom,
! [A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
thf(1740,plain,
! [A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(542,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
!= ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) @ B @ C )
| ( D = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
thf(1910,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
!= ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) @ B @ C )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_1) ).
thf(1360,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(742,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(626,axiom,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(2100,plain,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Hilbert__Choice_OEps @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_someI_0) ).
thf(1259,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Hilbert__Choice_OEps @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(1328,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(195,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ A @ B ) )
= B )
| ~ ( c_Lattices_Oboolean__algebra @ C @ A @ D @ E @ F @ G @ H @ I @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Odouble__compl_0) ).
thf(1121,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ A @ B ) )
= B )
| ~ ( c_Lattices_Oboolean__algebra @ C @ A @ D @ E @ F @ G @ H @ I @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(1064,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(1227,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(383,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Inductive_Ocomplete__lattice_Olfp @ A @ B @ C )
= ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ C @ ( tc_fun @ C @ C ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ C ) ) @ ( c_Collect @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ C ) @ ( tc_fun @ C @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ C @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ C ) ) @ ( c_COMBS @ C @ C @ tc_bool ) ) @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ C @ tc_bool ) @ C ) @ B ) ) ) @ ( c_COMBI @ C ) ) ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ B @ E @ F @ G @ H @ I @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Olfp__def__raw_0) ).
thf(1540,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Inductive_Ocomplete__lattice_Olfp @ A @ B @ C )
= ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ C @ ( tc_fun @ C @ C ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ C ) ) @ ( c_Collect @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ C @ C ) @ ( tc_fun @ C @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ C @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ C ) ) @ ( c_COMBS @ C @ C @ tc_bool ) ) @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ C @ tc_bool ) @ C ) @ B ) ) ) @ ( c_COMBI @ C ) ) ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ B @ E @ F @ G @ H @ I @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__INT_0) ).
thf(1138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(475,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(1755,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(42,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__UN__flatten_0) ).
thf(783,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(874,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(634,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
thf(2115,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(380,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_FuncSet_Oextensional @ A @ B @ C )
= ( hAPP @ ( c_Collect @ ( tc_fun @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ ( tc_fun @ B @ C ) ) @ ( c_All @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ C ) ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ B ) @ c_Not ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ C ) @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ C ) ) @ ( c_COMBC @ B @ C @ tc_bool ) ) @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ C @ tc_bool ) @ B ) @ ( c_fequal @ C ) ) ) ) @ ( c_HOL_Oundefined @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_extensional__def_0) ).
thf(1534,plain,
! [C: $i,B: $i,A: $i] :
( ( c_FuncSet_Oextensional @ A @ B @ C )
= ( hAPP @ ( c_Collect @ ( tc_fun @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ ( tc_fun @ B @ C ) ) @ ( c_All @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ C ) ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ B ) @ c_Not ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ A ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ B @ C ) @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ C ) ) @ ( c_COMBC @ B @ C @ tc_bool ) ) @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ C @ tc_bool ) @ B ) @ ( c_fequal @ C ) ) ) ) @ ( c_HOL_Oundefined @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(1017,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(131,axiom,
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ t_b )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ t_a @ t_b ) @ v_A ) @ v_f )
= ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ t_b ) @ ( hAPP @ ( c_Set_Oimage @ v_f @ t_a @ t_b ) @ v_A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUPR__def__raw_0) ).
thf(980,plain,
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ t_b )
| ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ t_a @ t_b ) @ v_A ) @ v_f )
= ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ t_b ) @ ( hAPP @ ( c_Set_Oimage @ v_f @ t_a @ t_b ) @ v_A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(363,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__UNIV_0) ).
thf(1498,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(184,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 ) @ E ) @ ( hAPP @ F @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__E_0) ).
thf(1096,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 ) @ E ) @ ( hAPP @ F @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(440,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1672,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(395,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(1567,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(444,axiom,
class_Orderings_Otop @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
thf(1683,plain,
class_Orderings_Otop @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(154,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/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1028,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)],[154]) ).
thf(556,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I2_J_1) ).
thf(1942,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(346,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ C ) @ D ) ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ E ) ) ) ) @ C ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__bex_0) ).
thf(1461,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ C ) @ D ) ) @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ E ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ E ) ) ) ) @ C ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ E @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ C ) ) ) ) @ D ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1 @ C @ D @ B @ A ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__bex_2) ).
thf(901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ C ) ) ) ) @ D ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1 @ C @ D @ B @ A ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(329,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) )
= ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(1424,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) )
= ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
thf(1584,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(235,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
thf(1214,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1155,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)],[209]) ).
thf(327,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/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(1419,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)],[327]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B )
!= ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).
thf(1292,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B )
!= ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(111,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( C = D )
| ( C = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(933,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( C = D )
| ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(604,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ B ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__not_1) ).
thf(2053,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ B ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(669,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Lattices_Oboolean__algebra @ D @ A @ E @ F @ G @ H @ C @ B @ I ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__top__eq_0) ).
thf(2196,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Lattices_Oboolean__algebra @ D @ A @ E @ F @ G @ H @ C @ B @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(513,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( 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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).
thf(1842,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( 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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(490,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D )
= ( hAPP @ ( c_Collect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ B ) @ ( c_All @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) ) @ ( c_in @ B ) ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__def_0) ).
thf(1791,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D )
= ( hAPP @ ( c_Collect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ B ) @ ( c_All @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) ) @ ( c_in @ B ) ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(657,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Fun_Oinj__on @ C @ A @ B @ D )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ C @ B @ D ) @ A ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
thf(2172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Fun_Oinj__on @ C @ A @ B @ D )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ C @ B @ D ) @ A ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(631,axiom,
class_Lattices_Olower__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(2108,plain,
class_Lattices_Olower__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(597,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(2038,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(1207,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(618,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
thf(2085,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(414,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D )
!= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I2_J_0) ).
thf(1612,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D )
!= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(1039,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(274,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(1297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(738,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(378,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I2_J_1) ).
thf(1530,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(649,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(2153,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(199,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1131,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(226,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(1192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(1050,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(911,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(558,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(1947,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(573,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(518,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).
thf(1852,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(331,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/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
thf(1429,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)],[331]) ).
thf(459,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
thf(1715,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(461,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/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(1720,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)],[461]) ).
thf(644,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ D ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(2140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ D ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(1627,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(506,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(1825,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(286,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Set_Ovimage @ C @ A @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ C @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).
thf(1324,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Set_Ovimage @ C @ A @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ C @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(1263,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(404,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( ( c_Hilbert__Choice_OGreatestM @ B @ C @ D @ A )
= ( c_Hilbert__Choice_OEps @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBC @ D @ A @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_bool ) @ D ) @ ( c_lessequals @ A ) ) @ B ) ) ) @ B ) ) ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GreatestM__def_0) ).
thf(1588,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( ( c_Hilbert__Choice_OGreatestM @ B @ C @ D @ A )
= ( c_Hilbert__Choice_OEps @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBC @ D @ A @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_bool ) @ D ) @ ( c_lessequals @ A ) ) @ B ) ) ) @ B ) ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(133,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(985,plain,
class_Lattices_Obounded__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(1150,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(253,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert__distrib_0) ).
thf(1249,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(409,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) ) @ E ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_1) ).
thf(1599,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) ) @ E ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(251,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ A ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ B @ tc_bool ) @ D ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I10_J_0) ).
thf(1246,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ A ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ B @ tc_bool ) @ D ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(248,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(1241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(674,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(2208,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(450,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(1695,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ C ) ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__disjI_1) ).
thf(921,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ C ) ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(216,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ ( hAPP @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
thf(1170,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ ( hAPP @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(173,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(1071,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(224,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(679,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 ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_bool ) ) @ E ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__D_0) ).
thf(2221,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 ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ F @ tc_bool ) ) @ E ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(665,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(2189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
thf(773,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)],[38]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( ( c_Hilbert__Choice_OLeastM @ B @ C @ D @ A )
= ( c_Hilbert__Choice_OEps @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ A ) @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ A ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBB @ A @ tc_bool @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_bool ) @ D ) @ ( c_lessequals @ A ) ) @ B ) ) ) @ B ) ) ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LeastM__def_0) ).
thf(926,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( ( c_Hilbert__Choice_OLeastM @ B @ C @ D @ A )
= ( c_Hilbert__Choice_OEps @ ( hAPP @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_and ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ A ) @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ A ) @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( c_COMBB @ A @ tc_bool @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ tc_bool ) @ D ) @ ( c_lessequals @ A ) ) @ B ) ) ) @ B ) ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup_0) ).
thf(1434,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(520,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Ovimage @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ ( tc_fun @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ B @ ( tc_fun @ B @ B ) ) @ A ) @ ( c_HOL_OIf @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) @ D ) ) @ E ) @ A @ B ) @ F )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ F ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__if_2) ).
thf(1857,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Ovimage @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ ( tc_fun @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ B @ ( tc_fun @ B @ B ) ) @ A ) @ ( c_HOL_OIf @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) @ D ) ) @ E ) @ A @ B ) @ F )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ F ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(576,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(1991,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ ( hAPP @ ( c_Set_Ovimage @ B @ C @ A ) @ D ) ) ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
thf(1318,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ ( hAPP @ ( c_Set_Ovimage @ B @ C @ A ) @ D ) ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(672,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
thf(2203,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(501,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/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(1814,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)],[501]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).
thf(1086,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(606,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(2057,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(458,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ C )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ B @ F @ G @ A @ H @ D @ I @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__inf__bot_0) ).
thf(1712,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ C )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ B @ F @ G @ A @ H @ D @ I @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(516,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Lattices_Oboolean__algebra @ D @ A @ E @ F @ G @ H @ B @ C @ I ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__bot__eq_0) ).
thf(1846,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Lattices_Oboolean__algebra @ D @ A @ E @ F @ G @ H @ B @ C @ I ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(269,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1286,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ( c_Hilbert__Choice_OEps @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_some__sym__eq__trivial_0) ).
thf(1035,plain,
! [B: $i,A: $i] :
( ( c_Hilbert__Choice_OEps @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
thf(1026,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(537,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Lattices_Oboolean__algebra @ A @ B @ C @ D @ E @ F @ ( hAPP @ ( hAPP @ E @ G ) @ H ) @ ( hAPP @ ( hAPP @ F @ G ) @ H ) @ I )
| ( ( hAPP @ B @ G )
= H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__unique_0) ).
thf(1895,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Lattices_Oboolean__algebra @ A @ B @ C @ D @ E @ F @ ( hAPP @ ( hAPP @ E @ G ) @ H ) @ ( hAPP @ ( hAPP @ F @ G ) @ H ) @ I )
| ( ( hAPP @ B @ G )
= H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ A ) ) @ B ) @ C ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ B @ v_x ) ) @ ( hAPP @ C @ v_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
thf(718,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ A ) ) @ B ) @ C ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ B @ v_x ) ) @ ( hAPP @ C @ v_x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(90,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ B @ D @ E ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).
thf(888,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ B @ D @ E ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(636,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/sandbox/benchmark/theBenchmark.p',cls_Pi__mem_0) ).
thf(2121,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)],[636]) ).
thf(581,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(2001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(369,axiom,
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ v_a ) @ v_B )
= ( hAPP @ ( c_Collect @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_or ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ t_a @ tc_bool ) @ ( c_fequal @ t_a ) ) @ v_a ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__compr__raw_0) ).
thf(1510,plain,
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ t_a ) @ v_a ) @ v_B )
= ( hAPP @ ( c_Collect @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_or ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ t_a @ tc_bool ) @ ( c_fequal @ t_a ) ) @ v_a ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(478,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1764,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(443,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).
thf(1680,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(595,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
thf(2033,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(824,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).
thf(1273,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
thf(856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(27,axiom,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
thf(745,plain,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1,negated_conjecture,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_HOL_Oord__class_Oless @ tc_nat ) ) @ v_h____ ) ) @ v_n ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) @ ( hAPP @ ( c_Collect @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) @ tc_bool @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_All @ tc_Arrow__Order__Mirabelle_Oindi ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) @ tc_bool ) @ ( c_in @ tc_Arrow__Order__Mirabelle_Oindi ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_bool ) @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(689,plain,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_HOL_Oord__class_Oless @ tc_nat ) ) @ v_h____ ) ) @ v_n ) ) ) @ v_Lab____ ) ) @ v_Lba____ ) ) @ ( hAPP @ ( c_Collect @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) @ tc_bool @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_All @ tc_Arrow__Order__Mirabelle_Oindi ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( hAPP @ ( c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) @ tc_bool ) @ ( c_in @ tc_Arrow__Order__Mirabelle_Oindi ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_bool ) @ tc_bool ) ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_bool ) @ tc_bool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_bool ) @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ) ) @ c_Arrow__Order__Mirabelle_OLin ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ ( c_COMBI @ A ) @ A @ A ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__ident_0) ).
thf(1374,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ ( c_COMBI @ A ) @ A @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(201,axiom,
! [A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).
thf(1135,plain,
! [A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(1648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(451,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1698,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
thf(1103,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(387,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/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(1548,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)],[387]) ).
thf(549,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( hAPP @ ( c_Collect @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_1) ).
thf(1927,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( hAPP @ ( c_Collect @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(593,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
thf(2028,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(407,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(1595,plain,
class_Lattices_Oupper__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(509,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(1833,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(544,axiom,
! [A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( c_Lattices_Oboolean__algebra @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ A ) ) @ A ) @ ( c_COMBB @ A @ A @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ A ) ) @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_lessequals @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_HOL_Oord__class_Oless @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dual__boolean__algebra_0) ).
thf(1916,plain,
! [A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( c_Lattices_Oboolean__algebra @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ A ) ) @ A ) @ ( c_COMBB @ A @ A @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ A ) ) @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_lessequals @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_HOL_Oord__class_Oless @ A ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(602,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(2048,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(732,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(843,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(417,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(1620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(550,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ B @ tc_bool ) @ A ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ A @ D ) @ C ) ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I10_J_0) ).
thf(1929,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ D @ ( tc_fun @ B @ tc_bool ) @ A ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ F @ A @ D ) @ C ) ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(826,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ B ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ B ) ) @ ( hAPP @ ( c_Collect @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conj__eq_0) ).
thf(1403,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ B ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ B ) ) @ ( hAPP @ ( c_Collect @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(1124,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(144,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
thf(1007,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).
thf(694,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)],[4]) ).
thf(415,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_0) ).
thf(1615,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(487,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(1784,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(492,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ C ) ) @ D )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
thf(1795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ C ) ) @ D )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(453,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(1701,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(652,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ C ) @ D ) ) @ A )
| ~ ( hBOOL @ ( hAPP @ E @ D ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ E ) ) ) @ C ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ B ) @ E ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__bounded__ex_0) ).
thf(2161,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ C ) @ D ) ) @ A )
| ~ ( hBOOL @ ( hAPP @ E @ D ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ E ) ) ) @ C ) ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ B ) @ E ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
thf(936,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(456,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).
thf(1707,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ B ) ) @ C ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__conjI_0) ).
thf(1107,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ B ) ) @ C ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(579,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(1997,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(605,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2 @ B @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UNIV_1) ).
thf(2055,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2 @ B @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(947,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1224,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(647,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
thf(2148,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(439,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1669,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(667,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(2193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(488,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq_0) ).
thf(1786,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
thf(1271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
thf(1371,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(424,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ ( hAPP @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__lower_0) ).
thf(1635,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ ( hAPP @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( hAPP @ ( c_Collect @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectD_0) ).
thf(1733,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( hAPP @ ( c_Collect @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(654,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(2166,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(1090,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
thf(919,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__def_0) ).
thf(804,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(616,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(2079,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ A @ B @ C ) ) @ 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 ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__Lin_0) ).
thf(831,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_Arrow__Order__Mirabelle_Obelow @ A @ B @ C ) ) @ 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 ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(676,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__singleton_0) ).
thf(2214,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(536,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
thf(1894,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(193,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(1117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(146,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(1011,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(1048,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(552,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__upper_0) ).
thf(1933,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(1043,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Hilbert__Choice_OEps @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ( ( c_Hilbert__Choice_OEps @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEps__psimp_0) ).
thf(1349,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_Hilbert__Choice_OEps @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ( ( c_Hilbert__Choice_OEps @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(624,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(2097,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(481,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(1771,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(23,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 ) @ c_Arrow__Order__Mirabelle_OLin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linear__alt_0) ).
thf(737,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 ) @ c_Arrow__Order__Mirabelle_OLin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(397,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__Un_0) ).
thf(1571,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(307,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ B ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__neg__eq_0) ).
thf(1376,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ B ) )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(567,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/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1969,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)],[567]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( c_fequal @ A ) @ B ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if2_0) ).
thf(1307,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( c_fequal @ A ) @ B ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(54,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__leI_0) ).
thf(811,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(529,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ D ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__iff_0) ).
thf(1877,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ D ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ ( tc_fun @ A @ tc_bool ) ) @ F ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(591,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(2025,plain,
class_Lattices_Oupper__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(639,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(2129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(577,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition2_0) ).
thf(1993,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(465,axiom,
! [B: $i,A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(1731,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)],[465]) ).
thf(522,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(1862,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(700,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(511,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(1838,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(102,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ D ) @ ( c_Set_Ovimage @ A @ B @ C ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__INT_0) ).
thf(915,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ D ) @ ( c_Set_Ovimage @ A @ B @ C ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ B ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ B ) ) ) @ ( hAPP @ ( c_Collect @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__imp__eq_0) ).
thf(1344,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ B ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Collect @ A ) @ B ) ) ) @ ( hAPP @ ( c_Collect @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(560,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_Collect @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_0) ).
thf(1952,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_Collect @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(504,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_COMBI @ A ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
thf(1820,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_COMBI @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(890,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(438,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(1667,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(758,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
thf(1339,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Set_Ovimage @ C @ A @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ ( hAPP @ C @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
thf(858,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Set_Ovimage @ C @ A @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ ( hAPP @ C @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(391,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_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(1557,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_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(49,axiom,
! [A: $i] :
( ( c_Predicate_OPowp @ A @ v_B @ t_a )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Powp__def_0) ).
thf(799,plain,
! [A: $i] :
( ( c_Predicate_OPowp @ A @ v_B @ t_a )
= ( hAPP @ ( c_All @ t_a ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ t_a @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ t_a ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ v_B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(726,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)],[18]) ).
thf(191,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(1112,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(447,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 @ ( hAPP @ ( hAPP @ B @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Lattices_Oboolean__algebra @ F @ A @ G @ H @ E @ B @ I @ J @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__sup_0) ).
thf(1688,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 @ ( hAPP @ ( hAPP @ B @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Lattices_Oboolean__algebra @ F @ A @ G @ H @ E @ B @ I @ J @ K ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(101,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 @ ( hAPP @ ( hAPP @ B @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Lattices_Oboolean__algebra @ F @ A @ G @ H @ B @ E @ I @ J @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__inf_0) ).
thf(912,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 @ ( hAPP @ ( hAPP @ B @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ ( hAPP @ A @ C ) ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Lattices_Oboolean__algebra @ F @ A @ G @ H @ B @ E @ I @ J @ K ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(132,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I7_J_0) ).
thf(983,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(316,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1396,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(452,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1699,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(959,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ B ) ) @ C ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__disjI_2) ).
thf(768,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_or ) @ B ) ) @ C ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(603,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(2051,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(88,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/sandbox/benchmark/theBenchmark.p',cls_extensional__arb_0) ).
thf(883,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)],[88]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(1176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(688,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C ) ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eq__UN_0) ).
thf(2244,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C ) ) @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(590,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).
thf(2022,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(353,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ B ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
thf(1477,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ B ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(627,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(2101,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(463,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(1726,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(362,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(1496,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( c_Collect @ A ) @ C ) )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Collect_0) ).
thf(851,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( c_Collect @ A ) @ C ) )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(650,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
thf(2156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(612,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(2069,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(393,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(1562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(1066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(81,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ E ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
thf(868,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_Set_Oimage @ C @ D @ B ) @ E ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(338,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(1445,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(377,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( c_fequal @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
thf(1528,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( c_fequal @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
thf(780,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(1643,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(609,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(2064,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(148,axiom,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_prod @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod__Finite__Set_Ofinite_Ofinite) ).
thf(1015,plain,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_prod @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(569,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/sandbox/benchmark/theBenchmark.p',cls_PiE_0) ).
thf(1973,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)],[569]) ).
thf(496,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ E @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__I_0) ).
thf(1805,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ E @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(420,axiom,
c_Fun_Oinj__on @ v_h____ @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injh_0) ).
thf(1626,plain,
c_Fun_Oinj__on @ v_h____ @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(686,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ A ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ C @ A ) ) @ D ) ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) @ ( c_Finite__Set_Osetsum @ B @ A ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ A ) @ D ) ) ) @ F ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__commute_0) ).
thf(2239,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ A ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ C @ A ) ) @ D ) ) @ E ) ) @ F )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ C @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) @ ( c_Finite__Set_Osetsum @ B @ A ) ) @ ( hAPP @ ( c_COMBC @ B @ C @ A ) @ D ) ) ) @ F ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(498,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_Hilbert__Choice_OEps @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exE__some_0) ).
thf(1809,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_Hilbert__Choice_OEps @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(1662,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(277,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Set_Ovimage @ C @ A @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ C @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).
thf(1304,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Set_Ovimage @ C @ A @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ C @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(944,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D ) @ B )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).
thf(795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D ) @ B )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(445,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(1684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(265,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 ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(1277,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 ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(177,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ C ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ D ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__right__distrib_0) ).
thf(1081,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ C ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ D ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(939,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ C ) )
| ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(351,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
thf(1472,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(205,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( hAPP @ ( c_Set_Ovimage @ A @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
thf(1145,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( hAPP @ ( c_Set_Ovimage @ A @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(30,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oboolean__algebra @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ A ) ) @ A ) @ ( c_COMBB @ A @ A @ A ) ) @ B ) ) @ C ) @ C @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ E ) @ B @ F @ G @ H @ A )
| ~ ( c_Lattices_Oboolean__algebra @ I @ C @ D @ E @ F @ B @ H @ G @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Odual__boolean__algebra_0) ).
thf(754,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oboolean__algebra @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ A @ A ) @ ( tc_fun @ A @ A ) ) @ A ) @ ( c_COMBB @ A @ A @ A ) ) @ B ) ) @ C ) @ C @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ E ) @ B @ F @ G @ H @ A )
| ~ ( c_Lattices_Oboolean__algebra @ I @ C @ D @ E @ F @ B @ H @ G @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(583,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/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).
thf(2005,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)],[583]) ).
thf(175,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(1076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(476,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
thf(1758,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) @ C )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
thf(1166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) @ C )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(126,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ E @ C ) ) )
| ~ ( c_Lattices_Oboolean__algebra @ A @ E @ F @ G @ D @ H @ I @ J @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Odiff__eq_0) ).
thf(968,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ D @ B ) @ ( hAPP @ E @ C ) ) )
| ~ ( c_Lattices_Oboolean__algebra @ A @ E @ F @ G @ D @ H @ I @ J @ K ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(221,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(1181,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(65,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ E @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__insert_0) ).
thf(836,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ E @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1551,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(515,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1845,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(372,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ C )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ B @ F @ G @ H @ A @ I @ D @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__sup__top_0) ).
thf(1516,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ C )
= D )
| ~ ( c_Lattices_Oboolean__algebra @ E @ B @ F @ G @ H @ A @ I @ D @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).
thf(872,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)],[83]) ).
thf(9,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ C @ I @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__UNIV_0) ).
thf(705,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ C @ I @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(666,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(2192,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).
thf(971,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(303,axiom,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(1368,plain,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(484,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(1780,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(474,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_Collect @ A ) @ D ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_2) ).
thf(1753,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_Collect @ A ) @ D ) ) ) )
| ~ ( hBOOL @ ( hAPP @ D @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(185,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I1_J_1) ).
thf(1098,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(137,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 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(993,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 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(386,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1547,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) ) @ D ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I2_J_0) ).
thf(776,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) ) @ D ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(472,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ C ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if_1) ).
thf(1748,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ C ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
thf(712,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(1003,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(242,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).
thf(1225,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(607,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) ) @ D ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I1_J_0) ).
thf(2060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) ) @ D ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(470,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(1743,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(318,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_Arrow__Order__Mirabelle_Oabove @ A @ B @ C ) ) @ 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 ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_above__Lin_0) ).
thf(1400,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_Arrow__Order__Mirabelle_Oabove @ A @ B @ C ) ) @ 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 ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(645,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/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(2143,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)],[645]) ).
thf(586,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(2012,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(954,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(254,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(1252,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(357,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(1484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(165,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
thf(1053,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ F ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ F ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(621,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(2092,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(332,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(1432,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(1186,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(1235,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)],[246]) ).
thf(678,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I5_J_0) ).
thf(2219,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(508,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(1830,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(539,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(434,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ E @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__iff_2) ).
thf(1658,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ E @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(118,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1 @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__witness_0) ).
thf(951,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1 @ A ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(600,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I7_J_0) ).
thf(2044,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(238,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ B @ A @ C ) @ E ) ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).
thf(1218,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ B @ A @ C ) @ E ) ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(291,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(1336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(239,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) )
= ( hAPP @ ( c_Set_Oimage @ D @ A @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__composition_0) ).
thf(1220,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) )
= ( hAPP @ ( c_Set_Oimage @ D @ A @ B ) @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__def_0) ).
thf(1300,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(425,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_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1637,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_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(198,axiom,
class_Lattices_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(1130,plain,
class_Lattices_Odistrib__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(400,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ C ) ) ) ) @ D ) ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( c_Collect @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__ball__eq_0) ).
thf(1579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ C ) ) ) ) @ D ) ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( c_Collect @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
thf(1358,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(562,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).
thf(1955,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(367,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I9_J_0) ).
thf(1506,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ ( tc_fun @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) ) @ E ) ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(864,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(330,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(1427,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(366,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 ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(1504,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 ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ A @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(493,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) )
= D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).
thf(1797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D ) )
= D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(460,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(1717,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(531,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I5_J_0) ).
thf(1881,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(77,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Set_Ovimage @ C @ A @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ C @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
thf(859,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( c_Set_Ovimage @ C @ A @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ ( hAPP @ C @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(384,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(1543,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(479,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(1766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(538,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 @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Lattices_Oboolean__algebra @ D @ A @ E @ F @ G @ H @ I @ J @ K )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_boolean__algebra_Ocompl__eq__compl__iff_0) ).
thf(1898,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 @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Lattices_Oboolean__algebra @ D @ A @ E @ F @ G @ H @ I @ J @ K )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(517,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(1849,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(1257,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1536,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(572,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ C @ ( hAPP @ ( c_Collect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ B ) ) ) ) @ ( hAPP @ ( c_COMBC @ D @ D @ tc_bool ) @ E ) ) ) ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ C @ A @ E @ F @ G @ H @ I @ J @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__Inf_0) ).
thf(1981,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ C @ ( hAPP @ ( c_Collect @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ tc_bool @ D ) @ ( c_All @ D ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ D @ tc_bool ) @ ( tc_fun @ D @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBS @ D @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ D ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ D @ ( tc_fun @ D @ tc_bool ) @ tc_bool ) @ ( c_in @ D ) ) @ B ) ) ) ) @ ( hAPP @ ( c_COMBC @ D @ D @ tc_bool ) @ E ) ) ) ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ C @ A @ E @ F @ G @ H @ I @ J @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(130,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(978,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
thf(1140,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
thf(991,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(416,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(1617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(555,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ B ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__not_0) ).
thf(1940,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ tc_bool @ A ) @ c_Not ) @ B ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(845,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
thf(1459,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(566,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).
thf(1966,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(110,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
thf(931,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(389,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(1553,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(502,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(1817,plain,
class_Lattices_Olattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(1412,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(237,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1216,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)],[237]) ).
thf(313,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I5_J_0) ).
thf(1390,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(524,axiom,
! [B: $i,A: $i] :
( ( c_Hilbert__Choice_OEps @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_some__eq__trivial_0) ).
thf(1866,plain,
! [B: $i,A: $i] :
( ( c_Hilbert__Choice_OEps @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(497,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Oboolean__algebra @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
thf(1807,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)],[497]) ).
thf(545,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(1918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(178,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(1084,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(1157,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(543,axiom,
! [A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(1913,plain,
! [A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(129,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 ) @ ( hAPP @ ( c_Set_Ovimage @ B @ E @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).
thf(976,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 ) @ ( hAPP @ ( c_Set_Ovimage @ B @ E @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(903,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(664,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(2187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(1189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(681,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(2226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1453,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(287,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(1326,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)],[287]) ).
thf(658,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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
thf(2174,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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(355,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(1481,plain,
class_Lattices_Olower__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(186,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
thf(1101,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D ) ) @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(422,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(1629,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(471,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).
thf(1745,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(592,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(2026,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(375,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Ovimage @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ ( tc_fun @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ B @ ( tc_fun @ B @ B ) ) @ A ) @ ( c_HOL_OIf @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) @ D ) ) @ E ) @ A @ B ) @ F )
= C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__if_1) ).
thf(1523,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Ovimage @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ ( tc_fun @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ B @ ( tc_fun @ B @ B ) ) @ A ) @ ( c_HOL_OIf @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) @ D ) ) @ E ) @ A @ B ) @ F )
= C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(138,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ D ) @ ( c_Set_Ovimage @ A @ B @ C ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UN_0) ).
thf(995,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ F ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ D ) @ ( c_Set_Ovimage @ A @ B @ C ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(123,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__Un_0) ).
thf(961,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(55,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ ( hAPP @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
thf(813,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ D @ F ) @ ( hAPP @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(311,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
thf(1385,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(963,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(655,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(2167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__unique_0) ).
thf(1341,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(896,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(748,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(441,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(1674,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ C )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__empty_0) ).
thf(1639,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ C )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(169,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1062,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(368,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ C ) ) ) ) @ D ) ) ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1 @ C @ D @ B @ A ) ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Collect__bex_1) ).
thf(1508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_Ex @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ B @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ B ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ B @ tc_bool ) @ tc_bool ) @ ( c_in @ B ) ) @ C ) ) ) ) @ D ) ) ) @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1 @ C @ D @ B @ A ) ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ B ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( c_Collect @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__all__eq_0) ).
thf(1244,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ B ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ B ) @ ( c_Collect @ A ) ) @ ( hAPP @ ( c_COMBC @ A @ B @ tc_bool ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(505,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if_0) ).
thf(1822,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(585,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
thf(2009,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(483,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( B
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
thf(1777,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( B
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(109,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 @ ( hAPP @ ( c_COMBC @ C @ C @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ C @ tc_bool ) @ E ) @ F @ G @ H @ I @ C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ A @ D @ E @ G @ F @ I @ H @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
thf(929,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 @ ( hAPP @ ( c_COMBC @ C @ C @ tc_bool ) @ D ) @ ( hAPP @ ( c_COMBC @ C @ C @ tc_bool ) @ E ) @ F @ G @ H @ I @ C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ A @ D @ E @ G @ F @ I @ H @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(610,axiom,
hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_Lba____ ) @ c_Arrow__Order__Mirabelle_OLin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(2066,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ v_Lba____ ) @ c_Arrow__Order__Mirabelle_OLin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(623,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(2095,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(1045,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2 @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__UNIV_2) ).
thf(1161,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(1030,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)],[155]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1491,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(662,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(2183,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(234,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 @ ( c_Inductive_Ocomplete__lattice_Olfp @ B @ A @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ D @ E ) ) @ E ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Olfp__lowerbound_0) ).
thf(1212,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 @ ( c_Inductive_Ocomplete__lattice_Olfp @ B @ A @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ D @ E ) ) @ E ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(412,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ E @ A ) @ F ) @ G ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ A ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ E @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ B ) @ ( c_COMBB @ A @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) ) ) @ F ) ) ) @ G ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__product_0) ).
thf(1607,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ E @ A ) @ F ) @ G ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ tc_bool ) @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ A ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ E @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ B @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ B ) @ ( c_COMBB @ A @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) ) ) @ F ) ) ) @ G ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(34,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( B = E )
| ( C = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(763,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( B = E )
| ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(683,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/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(2230,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)],[683]) ).
thf(596,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(2036,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(582,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ D @ ( hAPP @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(2003,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F )
= ( hAPP @ D @ ( hAPP @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(637,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I3_J_1) ).
thf(2123,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ E ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__Un__eq_0) ).
thf(999,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(628,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
thf(2102,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(563,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( c_Collect @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).
thf(1957,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( c_Collect @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(684,axiom,
( ~ ( class_HOL_Ouminus @ t_b )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ t_a @ t_b ) ) @ v_A ) @ v_x )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ t_b ) @ ( hAPP @ v_A @ v_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__Compl__def__raw_0) ).
thf(2233,plain,
( ~ ( class_HOL_Ouminus @ t_b )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ t_a @ t_b ) ) @ v_A ) @ v_x )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ t_b ) @ ( hAPP @ v_A @ v_x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Ouminus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ouminus @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ouminus) ).
thf(1148,plain,
! [B: $i,A: $i] :
( ( class_HOL_Ouminus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ouminus @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition_0) ).
thf(735,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(370,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1 @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__UNIV_1) ).
thf(1512,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(482,axiom,
! [B: $i,A: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1 @ B @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__eq__I_0) ).
thf(1774,plain,
! [B: $i,A: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1 @ B @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(406,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1593,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(1380,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(854,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(574,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(1986,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(252,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(1248,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ A ) ) @ C ) ) @ D )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__negf_0) ).
thf(790,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ A ) ) @ C ) ) @ D )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(50,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Ovimage @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ ( tc_fun @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ B @ ( tc_fun @ B @ B ) ) @ A ) @ ( c_HOL_OIf @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) @ D ) ) @ E ) @ A @ B ) @ F )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__if_0) ).
thf(801,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Ovimage @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ ( tc_fun @ B @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ B @ ( tc_fun @ B @ B ) ) @ A ) @ ( c_HOL_OIf @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ C ) ) ) @ D ) ) @ E ) @ A @ B ) @ F )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1363,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(449,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1693,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(535,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ A @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_0) ).
thf(1891,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ A @ B ) ) @ c_Arrow__Order__Mirabelle_OLin ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(680,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(2223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(886,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(1172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(323,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_Arrow__Order__Mirabelle_Omktop @ A @ B ) ) @ 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/sandbox/benchmark/theBenchmark.p',cls_mktop__Lin_0) ).
thf(1410,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_Arrow__Order__Mirabelle_Omktop @ A @ B ) ) @ 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)],[323]) ).
thf(156,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(1033,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(457,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ D @ ( hAPP @ A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).
thf(1710,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ D @ ( hAPP @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(228,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__empty_0) ).
thf(1197,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(598,axiom,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(2040,plain,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__range__imageI_0) ).
thf(696,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ C @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_Set_Oimage @ E @ C @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(1346,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(413,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Un_0) ).
thf(1610,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(1093,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(1352,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(261,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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
thf(1268,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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(382,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
!= ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ( D = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
thf(1537,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ D )
!= ( hAPP @ ( c_Set_Oimage @ A @ B @ C ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
thf(1378,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1019,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ B )
= ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_lessequals @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__Inf_0) ).
thf(908,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ B )
= ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) ) @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_lessequals @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(548,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
thf(1925,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(2,axiom,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_COMBI @ A ) @ B @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__id2_0) ).
thf(691,plain,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_COMBI @ A ) @ B @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(533,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf_0) ).
thf(1885,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(643,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(2138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(19,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(728,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ D @ A ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(507,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/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
thf(1827,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)],[507]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(1261,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(547,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(1923,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(16,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
thf(723,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(1331,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(1653,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(588,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(2018,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(326,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
thf(1416,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( ( hAPP @ D @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(1088,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(349,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(1468,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(1069,plain,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(10,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(708,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(659,axiom,
class_Lattices_Oboolean__algebra @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
thf(2177,plain,
class_Lattices_Oboolean__algebra @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(526,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( c_Collect @ C ) @ D ) )
= ( hAPP @ ( c_Collect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ tc_bool @ B ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Collect__eq_0) ).
thf(1870,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Ovimage @ A @ B @ C ) @ ( hAPP @ ( c_Collect @ C ) @ D ) )
= ( hAPP @ ( c_Collect @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ tc_bool @ B ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(557,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(1945,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(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) ) @ D ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__simps_I3_J_0) ).
thf(1009,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) ) @ D ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(106,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(923,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(673,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 ) @ ( hAPP @ ( c_Set_Ovimage @ B @ E @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).
thf(2206,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 ) @ ( hAPP @ ( c_Set_Ovimage @ B @ E @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(468,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( c_fequal @ A ) @ B ) ) ) @ C ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__conv__if2_1) ).
thf(1737,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_and ) @ ( hAPP @ ( c_fequal @ A ) @ B ) ) ) @ C ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(222,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv_0) ).
thf(1184,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ A @ tc_bool ) @ ( c_fequal @ A ) ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(614,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(2074,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(347,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_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ E @ A ) @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(1463,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_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ E @ A ) @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(394,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(1565,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(231,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(1204,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(340,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(1449,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(500,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP__UN__eq_0) ).
thf(1812,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ t_a @ tc_bool ) @ ( tc_fun @ t_a @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBC @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ ( c_in @ t_a ) ) ) @ B ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( tc_fun @ t_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(630,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(2106,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( hAPP @ ( c_Set_Oimage @ B @ C @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(619,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ B )
= ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) ) @ ( c_lessequals @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__Sup_0) ).
thf(2087,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ B )
= ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( hAPP @ ( c_Collect @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ tc_bool @ A ) @ ( c_All @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ tc_bool ) @ ( tc_fun @ A @ tc_bool ) @ A ) @ ( hAPP @ ( c_COMBS @ A @ tc_bool @ tc_bool ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_bool @ tc_bool ) @ A ) @ c_implies ) @ ( hAPP @ ( hAPP @ ( c_COMBC @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ ( c_in @ A ) ) @ B ) ) ) ) @ ( c_lessequals @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(2732,plain,
$false,
inference(e,[status(thm)],[1879,1024,1369,2072,1995,1729,1840,1315,1950,1686,2163,892,2199,1322,1665,1586,1501,809,1168,760,2109,2131,2031,1559,1105,1818,1295,1005,2062,1443,1073,1544,1142,1437,1855,1200,2077,1596,1406,2104,730,1290,1422,1569,2099,1591,1971,1793,1533,1041,861,1788,1655,1310,1735,715,1275,1872,1233,698,1988,1761,1954,2042,2146,1222,2195,1705,1999,797,898,2216,1001,2046,1576,1441,973,1935,2082,1475,1366,2067,1803,1482,829,1095,1243,1127,1782,2020,841,1650,1645,2136,1904,1265,1703,1287,1660,785,1907,1860,838,2126,949,724,1055,1409,917,702,751,1313,1279,2185,1455,1059,1132,1800,853,1479,1115,1931,2158,1641,1494,1963,1875,2169,1514,1319,870,1013,770,1398,881,2007,2178,924,1465,2090,2236,1334,834,1864,1978,1383,1677,1283,821,905,1489,1415,1302,756,1811,1450,1109,1632,1960,806,1581,966,766,1843,1215,866,1394,1526,2242,1405,849,1521,1975,877,692,1447,956,1119,1622,1604,942,1691,1438,793,1306,1153,2118,1783,1470,2093,1768,1868,1057,1163,894,952,1519,1355,1255,1487,815,1883,1387,1723,1021,778,1174,2133,1502,1751,820,788,2150,1238,2015,1602,1920,879,1555,1178,1888,1457,1624,2200,1159,1210,1079,1281,1573,1938,847,1836,2181,1195,2211,1392,2228,2112,710,1740,1910,1360,742,2100,1259,1328,1121,1064,1227,1540,1138,1755,783,989,874,2115,1534,1017,980,1498,1096,1672,1567,1683,1028,1942,1461,901,1424,1584,1214,1155,1419,1292,933,2053,2196,1842,1791,2172,2108,2038,1207,2085,1612,1039,1297,738,1530,2153,1131,1192,1050,911,721,1947,1984,1852,1429,1715,1720,2140,1627,1825,1324,1263,997,1588,985,1150,1249,1599,1246,1241,2208,1695,921,1170,1071,1187,2221,2189,773,926,1434,1857,1991,1318,1202,2203,1814,1086,2057,1712,1846,1286,1035,1026,1895,718,888,2121,2001,1510,1764,1680,2033,824,1273,856,745,689,1374,1135,1648,1698,1103,1548,1927,2028,1595,1833,1916,2048,732,843,1620,1929,826,1403,1124,1007,694,1615,1784,1795,1701,2161,936,1707,1107,1997,2055,947,1224,2148,1669,2193,1786,1271,1371,1635,1733,2166,1090,919,804,2079,831,2214,1894,1117,1011,1048,1933,1043,1349,2097,1771,737,1571,1376,1969,1307,811,1877,2025,2129,1993,1731,1862,700,1838,915,1344,1952,1820,890,1667,758,1339,858,1557,799,726,1112,1688,912,983,1396,1699,959,768,2051,883,1176,986,2244,2022,1477,2101,1726,1496,851,2156,2069,1562,1066,868,1445,1528,780,1643,2064,1015,1973,1805,1626,2239,1809,1662,1304,944,795,1684,1277,1081,939,1472,1145,754,2005,1076,1758,1166,968,1181,836,1551,1845,1516,872,705,2192,971,1368,1780,1753,1098,993,1547,776,1748,712,1003,1225,2060,1743,1400,2143,2012,954,1252,1230,1484,1053,2092,1432,1186,1235,2219,1830,1901,1658,951,2044,1218,1336,1220,1300,1637,1130,1579,1358,1955,1506,864,1427,1504,1797,1717,1881,859,1543,1766,1898,1849,1257,1536,1981,978,1140,991,1617,1940,845,1459,1966,931,1553,1817,1412,1216,1390,1866,1807,1918,1084,1157,1913,976,903,2187,1189,2226,1453,1326,2174,1481,1101,1629,1745,2026,1523,995,961,813,1385,963,2167,1341,896,748,1674,1639,1062,1508,1244,1822,2009,1777,929,2066,2095,1045,1161,1030,1491,2183,1212,1607,763,2230,2036,2003,2123,999,2102,1957,2233,818,1148,735,1512,1774,1593,1380,854,1986,1248,790,801,1363,1693,1891,2223,886,1172,1410,1033,1710,1197,2040,696,1346,1610,1093,1352,1268,1537,1378,1019,908,1925,691,1885,2138,728,740,1827,1261,1923,723,1331,1653,2018,1037,1416,1088,1468,1069,708,2177,1870,1945,1009,923,2206,1737,1184,2074,1463,1565,1204,1449,1812,2106,2087]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SCT077-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 15:27:18 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.94/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.88/1.13 % [INFO] Parsing done (249ms).
% 1.88/1.14 % [INFO] Running in sequential loop mode.
% 2.50/1.34 % [INFO] eprover registered as external prover.
% 2.50/1.35 % [INFO] cvc4 registered as external prover.
% 2.50/1.35 % [INFO] Scanning for conjecture ...
% 2.88/1.51 % [INFO] Found a conjecture and 687 axioms. Running axiom selection ...
% 3.80/1.67 % [INFO] Axiom selection finished. Selected 687 axioms (removed 0 axioms).
% 4.45/1.88 % [INFO] Problem is propositional (TPTP CNF).
% 4.45/1.90 % [INFO] Type checking passed.
% 4.45/1.90 % [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 ...
% 51.46/12.07 % External prover 'e' found a proof!
% 51.46/12.07 % [INFO] Killing All external provers ...
% 51.46/12.07 % Time passed: 11548ms (effective reasoning time: 10926ms)
% 51.46/12.07 % 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)>
% 51.46/12.08 % Axioms used in derivation (687): cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_boolean__algebra_Ocompl__top__eq_0, cls_subset__insert_1, cls_UN__extend__simps_I3_J_1, cls_some__eq__trivial_0, cls_bot__fun__eq_0, cls_inj__image__mem__iff_1, cls_top__fun__eq_0, cls_inf__sup__absorb_0, clsarity_nat__HOL_Oord, cls_vimage__code_0, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_inf__sup__aci_I2_J_0, cls_finite__Collect__disjI_1, cls_PiE_0, cls_Int__absorb2_0, cls_minus__le__iff_0, cls_bex__UNIV_2, cls_Compl__subset__Compl__iff_1, cls_UN__simps_I1_J_1, cls_order__le__less__trans_0, cls_sup__ge1_0, cls_compl__sup_0, cls_insertE_0, cls_UN__simps_I3_J_1, cls_SUPR__def__raw_0, cls_Un__subset__iff_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_equalityI_0, cls_boolean__algebra_Odiff__eq_0, cls_sup__top__left_0, cls_INT__simps_I7_J_0, cls_Collect__imp__eq_0, cls_insert__inter__insert_0, cls_boolean__algebra_Ocompl__sup__top_0, cls_xt1_I12_J_0, cls_COMBC__def_0, cls_subset__image__iff_2, cls_finite__insert_0, cls_inj__on__image__Int_0, cls_empty__is__image_1, cls_image__mono_0, clsarity_nat__Lattices_Odistrib__lattice, cls_le__funD_0, cls_subset__empty_1, cls_Pi__mem_0, cls_INT__extend__simps_I9_J_0, cls_vimage__UN_0, cls_square__eq__iff_1, cls_inj__image__eq__iff_0, cls_sup__bot__right_0, cls_insert__code_1, cls_Un__empty__left_0, cls_INT__extend__simps_I5_J_0, cls_ball__UNIV_2, cls_INT__D_0, clsarity_bool__Lattices_Olower__semilattice, cls_finite__vimageI_0, cls_le__SUPI_0, cls_boolean__algebra_Ocompl__bot__eq_0, cls_UN__extend__simps_I5_J_0, cls_Un__upper1_0, cls_UN__extend__simps_I10_J_0, cls_Un__commute_0, cls_fun__Compl__def_0, cls_image__Int_0, cls_UnCI_1, cls_Compl__eq_0, cls_distrib__sup__le_0, cls_Int__mono_0, cls_linorder__neqE_0, cls_mkbot__Lin_0, cls_le__iff__inf_1, cls_complete__lattice_OSup__singleton_0, cls_CHAINED_0, cls_inf__sup__aci_I6_J_0, clsarity_fun__Orderings_Oorder, cls_finite__Un_2, cls_Int__insert__left_0, cls_finite__Collect__disjI_0, cls_empty__iff_0, cls_Int__subset__iff_2, cls_le__inf__iff_1, cls_vimage__Collect__eq_0, cls_boolean__algebra_Ocompl__inf__bot_0, cls_mem__def_1, clsarity_nat__Orderings_Olinorder, cls_Int__Collect_1, cls_Inf__lower_0, cls_insert__absorb_0, cls_image__vimage__subset_0, cls_less__supI1_0, cls_Int__Un__distrib2_0, cls_compl__eq__compl__iff_0, cls_inf1E_1, cls_minus__minus_0, cls_insert__iff_1, cls_insert__subset_0, cls_sup__inf__distrib2_0, clsarity_fun__Lattices_Oupper__semilattice, cls_inj__image__subset__iff_0, cls_inj__on__Un__image__eq__iff_0, cls_less__minus__iff_0, cls_Collect__conj__eq_0, cls_LeastM__def_0, cls_inf__sup__distrib1_0, cls_vimage__UNIV_0, cls_order__less__trans_0, cls_vimage__if_3, cls_class__semiring_Osemiring__rules_I14_J_0, cls_neg__less__iff__less_1, cls_Int__absorb1_0, cls_le__sup__iff_0, cls_ComplD_0, cls_set__rev__mp_0, cls_inf__left__commute_0, cls_pred__equals__eq_0, cls_CollectI_0, cls_inf__commute_0, cls_UN__simps_I1_J_0, cls_inj__image__mem__iff_0, cls_sup__compl__top_0, cls_Collect__neg__eq_0, cls_mult__less__cancel__right__disj_3, clsarity_fun__Orderings_Otop, cls_INF__leI_0, cls_INFI__def__raw_0, cls_finite__insert_1, cls_finite__Collect__bex_0, cls_Compl__partition_0, cls_COMBB__def_0, cls_INT__absorb_0, cls_disjoint__eq__subset__Compl_0, cls_vimage__Compl_0, cls_subset__insert__iff_2, cls_INT__insert__distrib_0, cls_inj__image__Compl__subset_0, cls_Un__left__commute_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_nat__less__cases_0, cls_COMBS__def_0, cls_bex__UNIV_1, cls_finite__Int_1, cls_Int__empty__right_0, cls_neg__equal__iff__equal_0, cls_vimage__insert_0, cls_Collect__empty__eq_0, cls_INT__empty_0, cls_UN__extend__simps_I1_J_0, cls_CollectD_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_Un__Int__distrib2_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_INT__subset__iff_0, cls_Union__disjoint_0, cls_UN__singleton_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_order__less__asym_0, cls_inf__fun__eq_0, cls_linorder__not__less_0, cls_compl__bot__eq_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_empty__is__image_0, cls_neg__sup__eq__inf_0, cls_order__le__less_0, cls_rangeI_0, cls_order__less__asym_H_0, cls_Int__UN__distrib_0, cls_rev__image__eqI_0, cls_linorder__antisym__conv1_0, cls_class__semiring_Omul__c_0, cls_le__supE_1, cls_UN__iff_2, cls_linorder__antisym__conv2_0, cls_UN__extend__simps_I3_J_0, cls_order__eq__refl_0, cls_inj__on__insert_0, cls_finite__range__imageI_0, cls_range__composition_0, cls_SUP1__I_0, cls_UN__absorb_0, clsarity_fun__Orderings_Obot, cls_UN__simps_I3_J_0, cls_le__iff__sup_0, cls_dual__boolean__algebra_0, cls_Sup__UNIV_0, cls_minus__less__iff_1, cls_UN__insert__distrib_0, cls_Un__UNIV__right_0, cls_setsum__product_0, cls_Union__upper_0, cls_some__sym__eq__trivial_0, cls_Un__absorb2_0, cls_linorder__neqE__nat_0, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_vimage__INT_0, cls_vimageI_0, cls_complete__lattice_OSup__Inf_0, cls_sup__eq__neg__inf_0, cls_fun__Compl__def__raw_0, cls_UNIV__eq__I_0, cls_Pi__def_0, cls_finite__Int_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_less__le__not__le_2, cls_xt1_I10_J_0, cls_le__minus__iff_0, cls_UN__extend__simps_I9_J_0, cls_UnCI_0, cls_Un__upper2_0, cls_Int__insert__right_1, cls_Compl__disjoint2_0, cls_not__less__iff__gr__or__eq_0, cls_inf__top__right_0, cls_Sup__singleton_0, cls_sup__eq__bot__eq2_0, cls_image__def__raw_0, cls_UN__Un_0, cls_boolean__algebra_Odouble__compl_0, cls_vimage__ident_0, cls_vimage__if_0, cls_singleton__iff_1, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_INT__extend__simps_I10_J_0, cls_Collect__mem__eq_0, cls_Compl__UN_0, cls_subset__empty_0, cls_Compl__INT_0, cls_subset__Compl__self__eq_1, cls_complete__lattice_OInf__UNIV_0, cls_inf__eq__top__eq1_0, cls_UN__simps_I10_J_0, cls_ATP__Linkup_OCOMBC__def_0, cls_finite_0, cls_complete__lattice_OInf__empty_0, cls_Powp__def_0, cls_subset__iff_0, cls_insert__code_2, cls_CHAINED_0_01, 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, clsarity_fun__Finite__Set_Ofinite_Ofinite, cls_compl__top__eq_0, cls_SUP1__iff_2, cls_inf__absorb2_0, clsarity_bool__Lattices_Oupper__semilattice, cls_class__semiring_Osemiring__rules_I15_J_0, cls_le__minus__iff_1, cls_vimage__singleton__eq_1, cls_minus__mult__commute_0, cls_UNIV__not__empty_0, cls_insert__compr_0, cls_Compl__disjoint_0, cls_Sup__binary_0, cls_ball__UNIV_1, cls_Int__Collect_0, cls_Un__insert__left_0, cls_inf__sup__ord_I2_J_0, cls_doubleton__eq__iff_2, cls_Compl__partition2_0, cls_someI_0, cls_xt1_I8_J_0, cls_UN__extend__simps_I1_J_1, cls_finite__surj_0, cls_finite__UnI_0, cls_boolean__algebra_Oinf__compl__bot_0, cls_inf__sup__aci_I3_J_0, 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% 51.46/12.08 % No. of inferences in proof: 1377
% 51.46/12.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11548 ms resp. 10926 ms w/o parsing
% 52.37/12.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 52.41/12.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------