TSTP Solution File: SWV843-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV843-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 12:18:52 EDT 2023
% Result : Unsatisfiable 69.83s 19.40s
% Output : Refutation 70.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1169
% Syntax : Number of formulae : 2211 ( 399 unt; 128 typ; 0 def)
% Number of atoms : 5121 (1242 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 44216 (2784 ~;3038 |; 0 &;38394 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 238 ( 238 >; 0 *; 0 +; 0 <<)
% Number of symbols : 130 ( 128 usr; 18 con; 0-6 aty)
% Number of variables : 7206 ( 0 ^;7206 !; 0 ?;7206 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(v_F_type,type,
v_F: $i ).
thf(t_a_type,type,
t_a: $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_in_type,type,
c_in: $i > $i > $i > $i ).
thf(v_x_type,type,
v_x: $i ).
thf(c_Hoare__Mirabelle_Ohoare__derivs_type,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).
thf(v_G_type,type,
v_G: $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple_type,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).
thf(t_b_type,type,
t_b: $i ).
thf(v_P_H_type,type,
v_P_H: $i ).
thf(v_c0_type,type,
v_c0: $i ).
thf(v_Q_H_type,type,
v_Q_H: $i ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_COMBS_type,type,
c_COMBS: $i > $i > $i > $i > $i > $i ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_Com_Ostate_type,type,
tc_Com_Ostate: $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
thf(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(v_P_type,type,
v_P: $i ).
thf(v_Q_type,type,
v_Q: $i ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
thf(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
thf(class_Ring__and__Field_Oidom_type,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(class_Int_Onumber__ring_type,type,
class_Int_Onumber__ring: $i > $o ).
thf(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
thf(tc_nat_type,type,
tc_nat: $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(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i ).
thf(class_Lattices_Olower__semilattice_type,type,
class_Lattices_Olower__semilattice: $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(class_Lattices_Oupper__semilattice_type,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(class_OrderedGroup_Ocancel__ab__semigroup__add_type,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Orderings_Oord__class_Omin_type,type,
c_Orderings_Oord__class_Omin: $i > $i ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(c_Orderings_Oord__class_Omax_type,type,
c_Orderings_Oord__class_Omax: $i > $i ).
thf(class_Ring__and__Field_Oring_type,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(c_Finite__Set_Olinorder__class_OMin_type,type,
c_Finite__Set_Olinorder__class_OMin: $i > $i ).
thf(c_Finite__Set_Ofold1_type,type,
c_Finite__Set_Ofold1: $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_OrderedGroup_Oab__semigroup__idem__mult_type,type,
c_OrderedGroup_Oab__semigroup__idem__mult: $i > $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add__join_type,type,
class_OrderedGroup_Olordered__ab__group__add__join: $i > $o ).
thf(c_Com_Ocom_OSemi_type,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(c_Com_Ocom_OSKIP_type,type,
c_Com_Ocom_OSKIP: $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Ocomm__semiring_type,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
thf(c_SetInterval_Oord__class_OatLeastAtMost_type,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OgreaterThanAtMost_type,type,
c_SetInterval_Oord__class_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(class_Lattices_Odistrib__lattice_type,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__add_type,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(class_Ring__and__Field_Opordered__ring_type,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(class_Lattices_Oboolean__algebra_type,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(c_Fun_Oinj__on_type,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(class_Ring__and__Field_Osemiring_type,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(class_Complete__Lattice_Ocomplete__lattice_type,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_Complete__Lattice_OInf__class_OInf_type,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
thf(c_Finite__Set_Ofold_type,type,
c_Finite__Set_Ofold: $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocancel__semigroup__add_type,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(c_Finite__Set_Olinorder__class_OMax_type,type,
c_Finite__Set_Olinorder__class_OMax: $i > $i ).
thf(c_Lattices_Olower__semilattice_type,type,
c_Lattices_Olower__semilattice: $i > $i > $i > $i > $o ).
thf(c_Fun_Ofun__upd_type,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__add__meet_type,type,
class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(class_HOL_Ominus_type,type,
class_HOL_Ominus: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__add_type,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(class_HOL_Oord_type,type,
class_HOL_Oord: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_Ring__and__Field_Osemiring__0_type,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(class_Finite__Set_Ofinite_Ofinite_type,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(v_sko__Hoare__Mirabelle__Xconseq12__1_type,type,
v_sko__Hoare__Mirabelle__Xconseq12__1: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq12__3_type,type,
v_sko__Hoare__Mirabelle__Xconseq12__3: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Osetsum_type,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(c_Nitpick_Osko__Nitpick__XEx1__def__1__3_type,type,
c_Nitpick_Osko__Nitpick__XEx1__def__1__3: $i > $i > $i ).
thf(c_Finite__Set_Ofold__graph_type,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__idem__mult_type,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3_type,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3: $i > $i > $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2_type,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1: $i > $i > $i > $i ).
thf(class_Orderings_Otop_type,type,
class_Orderings_Otop: $i > $o ).
thf(t_c_type,type,
t_c: $i ).
thf(v_R_type,type,
v_R: $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_Fun_Othe__inv__into_type,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ofold__image_type,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $i > $i ).
thf(c_OrderedGroup_Oab__semigroup__mult_type,type,
c_OrderedGroup_Oab__semigroup__mult: $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1_type,type,
c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq2__1_type,type,
v_sko__Hoare__Mirabelle__Xconseq2__1: $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq2__2_type,type,
v_sko__Hoare__Mirabelle__Xconseq2__2: $i > $i > $i ).
thf(c_Set_Ovimage_type,type,
c_Set_Ovimage: $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__ring__strict_type,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(v_sko__Hoare__Mirabelle__Xconseq1__1_type,type,
v_sko__Hoare__Mirabelle__Xconseq1__1: $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq1__2_type,type,
v_sko__Hoare__Mirabelle__Xconseq1__2: $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3_type,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3: $i > $i > $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2_type,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2: $i > $i > $i > $i > $i ).
thf(class_HOL_Ouminus_type,type,
class_HOL_Ouminus: $i > $o ).
thf(c_fequal_type,type,
c_fequal: $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq12__2_type,type,
v_sko__Hoare__Mirabelle__Xconseq12__2: $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(v_sko__Hoare__Mirabelle__Xescape__1_type,type,
v_sko__Hoare__Mirabelle__Xescape__1: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xescape__2_type,type,
v_sko__Hoare__Mirabelle__Xescape__2: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2_type,type,
c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2: $i > $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1_type,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1_type,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1_type,type,
c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1: $i > $i > $i > $i > $i ).
thf(c_Nitpick_Ofold__graph_H_type,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(757,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(2822,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
thf(1718,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(1823,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(392,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(1995,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)],[392]) ).
thf(909,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ B @ A ) ) @ C ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ A ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ A ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).
thf(3167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ B @ A ) ) @ C ) @ D ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ A ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ A ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(800,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I6_J_0) ).
thf(2921,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(1008,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(3397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(644,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ A ) ) @ ( c_Finite__Set_Ocard @ B @ A ) ) )
| ~ ( hBOOL @ ( c_in @ D @ B @ A ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff2__less_0) ).
thf(2559,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ A ) ) @ ( c_Finite__Set_Ocard @ B @ A ) ) )
| ~ ( hBOOL @ ( c_in @ D @ B @ A ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(541,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( 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_Diff__UNIV_0) ).
thf(2331,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( 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)],[541]) ).
thf(315,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_Lattices_Olower__semilattice @ ( c_COMBC @ ( c_lessequals @ A ) @ A @ A @ tc_bool ) @ ( c_COMBC @ ( c_HOL_Oord__class_Oless @ A ) @ A @ A @ tc_bool ) @ ( c_Orderings_Oord__class_Omax @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__lattice_0) ).
thf(1818,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_Lattices_Olower__semilattice @ ( c_COMBC @ ( c_lessequals @ A ) @ A @ A @ tc_bool ) @ ( c_COMBC @ ( c_HOL_Oord__class_Oless @ A ) @ A @ A @ tc_bool ) @ ( c_Orderings_Oord__class_Omax @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(1110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(504,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(2250,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)],[504]) ).
thf(842,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ C ) ) )
| ( hBOOL @ ( c_in @ B @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__insert_0) ).
thf(3021,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ C ) ) )
| ( hBOOL @ ( c_in @ B @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(109,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(1322,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)],[109]) ).
thf(221,axiom,
! [D: $i,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 ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
thf(1586,plain,
! [D: $i,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 ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(185,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(1501,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(1168,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(525,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(2295,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)],[525]) ).
thf(530,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ( hBOOL @ ( c_in @ D @ B @ A ) )
| ( hBOOL @ ( c_in @ D @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).
thf(2306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ( hBOOL @ ( c_in @ D @ B @ A ) )
| ( hBOOL @ ( c_in @ D @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(856,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(3053,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(837,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(3008,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)],[837]) ).
thf(441,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(2109,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Suc @ ( c_Finite__Set_Ocard @ B @ C ) ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_1) ).
thf(2031,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Suc @ ( c_Finite__Set_Ocard @ B @ C ) ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(241,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(1633,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)],[241]) ).
thf(738,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(2778,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)],[738]) ).
thf(425,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(2072,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(295,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(1767,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)],[295]) ).
thf(579,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(2412,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)],[579]) ).
thf(780,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(2876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(1237,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(742,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__binary_0) ).
thf(2787,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(658,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ E @ B ) ) @ ( c_Set_Ovimage @ A @ D @ E @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
thf(2595,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ E @ B ) ) @ ( c_Set_Ovimage @ A @ D @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(617,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
thf(2499,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(609,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(2480,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(387,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( hBOOL @ ( c_in @ D @ C @ F ) )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ F @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) ) @ E @ F @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).
thf(1982,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( hBOOL @ ( c_in @ D @ C @ F ) )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ F @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) ) @ E @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(374,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(1950,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)],[374]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(1549,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(289,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(1750,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)],[289]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
thf(1211,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(865,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(3072,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(975,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_HOL_Otimes__class_Otimes @ A ) @ A @ A ) @ B ) @ C ) )
| ( hBOOL @ ( c_in @ B @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__eq__fold_0) ).
thf(3317,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_HOL_Otimes__class_Otimes @ A ) @ A @ A ) @ B ) @ C ) )
| ( hBOOL @ ( c_in @ B @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(750,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(2808,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)],[750]) ).
thf(572,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ( ( hAPP @ ( c_Fun_Othe__inv__into @ B @ A @ C @ D ) @ ( hAPP @ A @ E ) )
= E )
| ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__f__eq_0) ).
thf(2395,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ( ( hAPP @ ( c_Fun_Othe__inv__into @ B @ A @ C @ D ) @ ( hAPP @ A @ E ) )
= E )
| ~ ( hBOOL @ ( c_in @ E @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(14,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(1073,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)],[14]) ).
thf(203,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(1544,plain,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(280,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(1728,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)],[280]) ).
thf(443,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(2114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(565,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
thf(2380,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(156,axiom,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(1437,plain,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
!= C )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
thf(1200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
!= C )
| ( B
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(427,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
| ( hBOOL @ ( c_in @ C @ ( c_Set_Oimage @ A @ F @ D @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).
thf(2077,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
| ( hBOOL @ ( c_in @ C @ ( c_Set_Oimage @ A @ F @ D @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).
thf(1290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(342,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(1882,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)],[342]) ).
thf(737,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(2776,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)],[737]) ).
thf(685,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(2659,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)],[685]) ).
thf(1017,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty_0) ).
thf(3417,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(656,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 ) @ ( c_Finite__Set_Osetsum @ C @ D @ E @ A ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C @ A @ A @ E ) @ D @ E @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__right__distrib_0) ).
thf(2590,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 ) @ ( c_Finite__Set_Osetsum @ C @ D @ E @ A ) )
= ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C @ A @ A @ E ) @ D @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).
thf(1401,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(1034,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).
thf(3460,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
thf(1569,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(370,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(1939,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)],[370]) ).
thf(437,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ominus @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
thf(2099,plain,
! [B: $i,A: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ominus @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(519,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ D @ E ) @ C ) ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ D @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__inf__iff_1) ).
thf(2282,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ D @ E ) @ C ) ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(224,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_OrderedGroup_Oab__semigroup__idem__mult @ ( c_Orderings_Oord__class_Omin @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__min_0) ).
thf(1591,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_OrderedGroup_Oab__semigroup__idem__mult @ ( c_Orderings_Oord__class_Omin @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(305,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(1793,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)],[305]) ).
thf(771,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(2854,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(1533,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(51,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(1173,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)],[51]) ).
thf(177,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(1486,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(151,axiom,
! [A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_OrderedGroup_Oab__semigroup__idem__mult @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__inf_0) ).
thf(1426,plain,
! [A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_OrderedGroup_Oab__semigroup__idem__mult @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(256,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
thf(1671,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(1608,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(36,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(1137,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)],[36]) ).
thf(697,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(2686,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(105,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ D @ E @ A ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ E ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greaterThanAtMost_0) ).
thf(1310,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ D @ E @ A ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ E ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(895,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Compl_0) ).
thf(3135,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(994,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( c_in @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B ) @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).
thf(3365,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( c_in @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B ) @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).
thf(1735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(984,axiom,
! [D: $i,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 ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ D @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__Un_0) ).
thf(3338,plain,
! [D: $i,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 ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ D @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ D @ ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(455,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ B @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infI2_0) ).
thf(2141,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ B @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).
thf(1872,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(73,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(1233,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)],[73]) ).
thf(599,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(2459,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)],[599]) ).
thf(791,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).
thf(2901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(458,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ A @ B @ C @ D ) @ E ) @ ( c_Set_Oinsert @ F @ G @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ A @ B @ C @ D ) @ E ) @ G ) ) )
| ( hBOOL @ ( c_in @ F @ G @ D ) )
| ~ ( c_Finite__Set_Ofinite @ G @ D )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__image__insert_0) ).
thf(2146,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ A @ B @ C @ D ) @ E ) @ ( c_Set_Oinsert @ F @ G @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ F ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ A @ B @ C @ D ) @ E ) @ G ) ) )
| ( hBOOL @ ( c_in @ F @ G @ D ) )
| ~ ( c_Finite__Set_Ofinite @ G @ D )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(165,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(1458,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)],[165]) ).
thf(183,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(1497,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)],[183]) ).
thf(479,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(2195,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)],[479]) ).
thf(840,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(3017,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)],[840]) ).
thf(888,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(3120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(1022,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(3429,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(335,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(1867,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)],[335]) ).
thf(475,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(2184,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)],[475]) ).
thf(913,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(3175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(607,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(2476,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)],[607]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
thf(1260,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1015,axiom,
class_Lattices_Oboolean__algebra @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
thf(3414,plain,
class_Lattices_Oboolean__algebra @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(293,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(1761,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)],[293]) ).
thf(117,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(1342,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)],[117]) ).
thf(244,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
!= B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
thf(1640,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
!= B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(652,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_Ominus__class_Ominus @ A ) @ B @ A @ ( tc_fun @ A @ A ) @ C ) @ D @ C @ A @ A ) @ E @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_Finite__Set_Osetsum @ B @ E @ C @ A ) ) @ ( c_Finite__Set_Osetsum @ D @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__subtractf_0) ).
thf(2580,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_Ominus__class_Ominus @ A ) @ B @ A @ ( tc_fun @ A @ A ) @ C ) @ D @ C @ A @ A ) @ E @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_Finite__Set_Osetsum @ B @ E @ C @ A ) ) @ ( c_Finite__Set_Osetsum @ D @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(1196,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(940,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A @ A ) @ B ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__Inf__fold__inf_0) ).
thf(3236,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A @ A ) @ B ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B )
= C )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 @ B @ C @ A ) @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__eqI_0) ).
thf(2020,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B )
= C )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 @ B @ C @ A ) @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(1036,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__belowI_0) ).
thf(3466,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(172,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(1475,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(755,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ ( c_Set_Ovimage @ B @ C @ D @ A ) @ D @ A ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
thf(2819,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ ( c_Set_Ovimage @ B @ C @ D @ A ) @ D @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
thf(1623,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(777,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(2869,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)],[777]) ).
thf(996,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(3370,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)],[996]) ).
thf(22,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(1095,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)],[22]) ).
thf(549,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(2348,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(988,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ E ) @ F @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ F ) )
| ~ ( hBOOL @ ( c_in @ E @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D ) )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__into_0) ).
thf(3350,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ E ) @ F @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ F ) )
| ~ ( hBOOL @ ( c_in @ E @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D ) )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(821,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
thf(2972,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(413,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(2046,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)],[413]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
thf(1243,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(731,axiom,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
!= ( c_Finite__Set_Ocard @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ( A
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).
thf(2763,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
!= ( c_Finite__Set_Ocard @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ( A
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(639,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(2548,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(301,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(1782,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)],[301]) ).
thf(493,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Ovimage @ B @ ( c_Set_Oinsert @ ( hAPP @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ D @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
thf(2227,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Ovimage @ B @ ( c_Set_Oinsert @ ( hAPP @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ D @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(137,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(1391,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)],[137]) ).
thf(218,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(1576,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(873,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(3088,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)],[873]) ).
thf(3,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ ( hAPP @ v_P_H @ v_x ) ) @ ( hAPP @ v_c0 @ v_x ) ) @ ( hAPP @ v_Q_H @ v_x ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ v_P_H @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ t_a ) @ v_c0 @ t_a @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ v_Q_H @ t_a @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ v_F @ t_a @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ t_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(1046,plain,
c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ ( hAPP @ v_P_H @ v_x ) ) @ ( hAPP @ v_c0 @ v_x ) ) @ ( hAPP @ v_Q_H @ v_x ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ v_P_H @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ t_a ) @ v_c0 @ t_a @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ v_Q_H @ t_a @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ v_F @ t_a @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ t_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(398,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(2010,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ 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__Diff__cancel2_0) ).
thf(1935,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(574,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ) @ ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) @ ( c_Finite__Set_Osetsum @ B @ E @ C @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ C )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un__Int_0) ).
thf(2400,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ) @ ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) @ ( c_Finite__Set_Osetsum @ B @ E @ C @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ C )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(423,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(2067,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)],[423]) ).
thf(453,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( c_in @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B ) @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).
thf(2136,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( c_in @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B ) @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(87,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(1265,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)],[87]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
thf(1628,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(1287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).
thf(1709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(921,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ A ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ B @ A ) ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
thf(3195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ A ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ B @ A ) ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).
thf(1430,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(719,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).
thf(2735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(853,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ E @ F @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(3046,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ E @ F @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(728,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ C ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__Un2_0) ).
thf(2755,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ C ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(618,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(2501,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image_0) ).
thf(1511,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).
thf(1826,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(106,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(1313,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)],[106]) ).
thf(391,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(1992,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)],[391]) ).
thf(852,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(3043,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(649,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(2571,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)],[649]) ).
thf(945,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
= ( c_Finite__Set_Ocard @ C @ D ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Set_Oimage @ E @ C @ D @ B ) ) @ A ) )
| ~ ( c_Fun_Oinj__on @ E @ C @ D @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ F @ A @ B @ D ) ) @ C ) )
| ~ ( c_Fun_Oinj__on @ F @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__bij__eq_0) ).
thf(3248,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
= ( c_Finite__Set_Ocard @ C @ D ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Set_Oimage @ E @ C @ D @ B ) ) @ A ) )
| ~ ( c_Fun_Oinj__on @ E @ C @ D @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ F @ A @ B @ D ) ) @ C ) )
| ~ ( c_Fun_Oinj__on @ F @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(925,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) ) @ ( c_Finite__Set_Ocard @ C @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__card__mono_0) ).
thf(3204,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) ) @ ( c_Finite__Set_Ocard @ C @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(8,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(1055,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)],[8]) ).
thf(144,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(1409,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)],[144]) ).
thf(540,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).
thf(2328,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(798,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B )
= ( c_Suc @ ( c_Finite__Set_Ocard @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_5) ).
thf(2916,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B )
= ( c_Suc @ ( c_Finite__Set_Ocard @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(410,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(2039,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)],[410]) ).
thf(956,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
thf(3275,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(703,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) @ ( hAPP @ B @ E ) ) )
| ~ ( hBOOL @ ( c_in @ E @ D @ C ) )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__ring_0) ).
thf(2698,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) @ ( hAPP @ B @ E ) ) )
| ~ ( hBOOL @ ( c_in @ E @ D @ C ) )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(252,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ G @ D @ E )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ F @ G @ D @ E ) @ B @ C @ D @ E ) )
| ( B = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
thf(1660,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ G @ D @ E )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ F @ G @ D @ E ) @ B @ C @ D @ E ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(886,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_4) ).
thf(3116,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(689,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(2667,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(112,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(1330,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)],[112]) ).
thf(489,axiom,
( ( hAPP @ ( hAPP @ ( c_COMBC @ v_P @ t_a @ t_b @ t_c ) @ v_Q ) @ v_R )
= ( hAPP @ ( hAPP @ v_P @ v_R ) @ v_Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def__raw_0) ).
thf(2217,plain,
( ( hAPP @ ( hAPP @ ( c_COMBC @ v_P @ t_a @ t_b @ t_c ) @ v_Q ) @ v_R )
= ( hAPP @ ( hAPP @ v_P @ v_R ) @ v_Q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(1013,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ A @ B @ D @ C @ E @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).
thf(3410,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ A @ B @ D @ C @ E @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(958,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(3280,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(789,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_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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_Diff__Int__distrib_0) ).
thf(2897,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_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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)],[789]) ).
thf(57,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ A )
= ( c_Finite__Set_Ofold1 @ ( c_Orderings_Oord__class_Omin @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__class_OMin__def__raw_0) ).
thf(1191,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ A )
= ( c_Finite__Set_Ofold1 @ ( c_Orderings_Oord__class_Omin @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(602,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ C ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__Un_0) ).
thf(2466,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ C ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(448,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(2126,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)],[448]) ).
thf(204,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(1545,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(710,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( 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 ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__Un_0) ).
thf(2713,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( 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 ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(40,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(1147,plain,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(803,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ C @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ C @ D )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
thf(2929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ C @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ C @ D )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(314,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
thf(1815,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(339,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(1875,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)],[339]) ).
thf(632,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(2533,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(953,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_1) ).
thf(3268,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(347,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(1892,plain,
class_HOL_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(1035,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(3463,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)],[1035]) ).
thf(998,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(3374,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)],[998]) ).
thf(1003,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_Orderings_Oord__class_Omin @ A ) @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_Orderings_Oord__class_Omin @ A ) @ A ) @ C ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__antimono_0) ).
thf(3385,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_Orderings_Oord__class_Omin @ A ) @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_Orderings_Oord__class_Omin @ A ) @ A ) @ C ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(468,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
thf(2169,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(575,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_1) ).
thf(2403,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(191,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(1514,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)],[191]) ).
thf(415,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 @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(2049,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 @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(641,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(2552,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__diff__distrib__left_0) ).
thf(1319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(270,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(1704,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)],[270]) ).
thf(346,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 ) @ ( c_Suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(1890,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 ) @ ( c_Suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(562,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(2373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
thf(1347,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(973,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(3312,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)],[973]) ).
thf(366,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(1931,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(214,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(1568,plain,
class_Lattices_Oupper__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(839,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(3014,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(716,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
= ( c_Set_Oimage @ ( c_COMBB @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(2730,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
= ( c_Set_Oimage @ ( c_COMBB @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(770,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
| ~ ( c_Lattices_Olower__semilattice @ F @ A @ B @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oless__infI2_0) ).
thf(2852,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ E ) )
| ~ ( c_Lattices_Olower__semilattice @ F @ A @ B @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(937,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ ( c_COMBB @ A @ B @ C @ D @ E ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__range__imageI_0) ).
thf(3231,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ ( c_COMBB @ A @ B @ C @ D @ E ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(397,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(2007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(491,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
thf(2222,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(977,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(3322,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(405,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(2027,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)],[405]) ).
thf(1006,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_6) ).
thf(3393,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(129,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(1373,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)],[129]) ).
thf(603,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(2469,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)],[603]) ).
thf(907,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).
thf(3163,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(1039,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__diff_0) ).
thf(3473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(782,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
thf(2880,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(319,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).
thf(1828,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(408,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oimage @ A @ F @ D @ E ) )
| ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).
thf(2034,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oimage @ A @ F @ D @ E ) )
| ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(543,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ C )
= B )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Set_Oimage @ A @ B @ C @ C ) ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).
thf(2335,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ C )
= B )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Set_Oimage @ A @ B @ C @ C ) ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(902,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(3152,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(401,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) )
| ~ ( c_Lattices_Olower__semilattice @ E @ F @ A @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__left__commute_0) ).
thf(2017,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) )
| ~ ( c_Lattices_Olower__semilattice @ E @ F @ A @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(812,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).
thf(2950,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(147,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(1415,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)],[147]) ).
thf(667,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Lattices_Olower__semilattice @ D @ E @ A @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__commute_0) ).
thf(2616,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_Lattices_Olower__semilattice @ D @ E @ A @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(168,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(1465,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)],[168]) ).
thf(866,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(3075,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(162,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(1450,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)],[162]) ).
thf(596,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(2451,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)],[596]) ).
thf(498,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ E @ B ) ) @ ( c_Set_Ovimage @ A @ D @ E @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
thf(2236,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ E @ B ) ) @ ( c_Set_Ovimage @ A @ D @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(331,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(1858,plain,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(1025,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(3438,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(523,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ D @ E ) @ C ) ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ D @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infE_1) ).
thf(2291,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ D @ E ) @ C ) ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(506,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Finite__Set_Ocard @ B @ A ) ) @ ( c_Finite__Set_Ocard @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__psubset_0) ).
thf(2254,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Finite__Set_Ocard @ B @ A ) ) @ ( c_Finite__Set_Ocard @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(378,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(1960,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(967,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(3300,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)],[967]) ).
thf(590,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ C @ D @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I22_J_0) ).
thf(2437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ C @ D @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(862,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(3068,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)],[862]) ).
thf(196,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
thf(1526,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(395,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ A @ B @ D @ C @ G @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ A @ B @ D @ C ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ G ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).
thf(2002,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ A @ B @ D @ C @ G @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ A @ B @ D @ C ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ G ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(439,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_Orderings_Oord__class_Omin @ A ) @ A ) @ D ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__below__fold1__iff_0) ).
thf(2103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_Orderings_Oord__class_Omin @ A ) @ A ) @ D ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(935,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).
thf(3226,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(228,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(1600,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(25,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(1104,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)],[25]) ).
thf(762,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(2833,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)],[762]) ).
thf(919,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(3189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(477,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(2190,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)],[477]) ).
thf(1019,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofold__graph @ C @ D @ A @ E @ B @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).
thf(3421,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofold__graph @ C @ D @ A @ E @ B @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(848,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(3036,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(631,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).
thf(2530,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(30,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(1119,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)],[30]) ).
thf(561,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(2371,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
thf(1394,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(904,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(3157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(521,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ominus @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ t_a @ A ) ) @ B ) @ C ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ B @ v_x ) ) @ ( hAPP @ C @ v_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
thf(2286,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ominus @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ t_a @ A ) ) @ B ) @ C ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ B @ v_x ) ) @ ( hAPP @ C @ v_x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(676,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
| ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ) @ D @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).
thf(2639,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
| ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ) @ D @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(979,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(3327,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)],[979]) ).
thf(154,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).
thf(1433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(928,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).
thf(3211,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(461,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(2154,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)],[461]) ).
thf(712,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_1) ).
thf(2718,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(1011,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(3406,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(484,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ C @ D @ A ) ) @ ( c_Set_Oimage @ B @ E @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(2205,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ C @ D @ A ) ) @ ( c_Set_Oimage @ B @ E @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(266,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(1696,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)],[266]) ).
thf(917,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(3184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(1024,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oinsert @ C @ ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ D @ tc_bool ) ) @ F ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ) @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).
thf(3435,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oinsert @ C @ ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ D @ tc_bool ) ) @ F ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ) @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ F @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(248,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(1651,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)],[248]) ).
thf(877,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D )
= ( c_Set_Oinsert @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ A ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(3097,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D )
= ( c_Set_Oinsert @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ A ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(1030,axiom,
( ( hAPP @ ( c_COMBB @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
= ( hAPP @ v_P @ ( hAPP @ v_Q @ v_R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def__raw_0) ).
thf(3450,plain,
( ( hAPP @ ( c_COMBB @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
= ( hAPP @ v_P @ ( hAPP @ v_Q @ v_R ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(795,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( c_Set_Oinsert @ C @ D @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ A @ B @ B ) @ C ) @ D ) )
| ( hBOOL @ ( c_in @ C @ D @ B ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__eq__fold_0) ).
thf(2910,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( c_Set_Oinsert @ C @ D @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ A @ B @ B ) @ C ) @ D ) )
| ( hBOOL @ ( c_in @ C @ D @ B ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(969,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(3303,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(605,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(2473,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)],[605]) ).
thf(264,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B @ F @ D @ E )
= ( c_Fun_Ofun__upd @ A @ B @ F @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
thf(1691,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B @ F @ D @ E )
= ( c_Fun_Ofun__upd @ A @ B @ F @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(650,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E )
!= A )
| ( ( hAPP @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
thf(2574,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E )
!= A )
| ( ( hAPP @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(910,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).
thf(3169,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(103,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(1306,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)],[103]) ).
thf(557,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(2364,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(918,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ B @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).
thf(3186,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ B @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(445,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(2118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(115,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(1338,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)],[115]) ).
thf(414,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(2047,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)],[414]) ).
thf(496,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) ) @ ( c_Finite__Set_Ocard @ C @ 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_card__mono_0) ).
thf(2232,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) ) @ ( c_Finite__Set_Ocard @ C @ 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)],[496]) ).
thf(677,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ D @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).
thf(2641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ D @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(838,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_Orderings_Oord__class_Omin @ A ) @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ D @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__below__iff_2) ).
thf(3011,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_Orderings_Oord__class_Omin @ A ) @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ D @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
thf(1206,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(170,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(1470,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)],[170]) ).
thf(434,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(2093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(12,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(1067,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(616,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 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(2496,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 ) ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(669,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(2621,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(743,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(2790,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)],[743]) ).
thf(793,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(2905,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)],[793]) ).
thf(566,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(2382,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)],[566]) ).
thf(420,axiom,
! [E: $i,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 ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).
thf(2061,plain,
! [E: $i,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 ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(736,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(2773,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)],[736]) ).
thf(394,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(2000,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)],[394]) ).
thf(4,negated_conjecture,
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ ( hAPP @ v_P @ v_x ) ) @ ( hAPP @ v_c0 @ v_x ) ) @ ( hAPP @ v_Q @ v_x ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ v_P @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ t_a ) @ v_c0 @ t_a @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ v_Q @ t_a @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ v_F @ t_a @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ t_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(1047,plain,
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ ( hAPP @ v_P @ v_x ) ) @ ( hAPP @ v_c0 @ v_x ) ) @ ( hAPP @ v_Q @ v_x ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ v_P @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ t_a ) @ v_c0 @ t_a @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ v_Q @ t_a @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ v_F @ t_a @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(281,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(1730,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)],[281]) ).
thf(849,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(3037,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(47,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(1163,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)],[47]) ).
thf(586,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) @ C @ A )
= ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) )
| ( hBOOL @ ( c_in @ E @ D @ C ) )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_1) ).
thf(2428,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) @ C @ A )
= ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) )
| ( hBOOL @ ( c_in @ E @ D @ C ) )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(193,axiom,
class_Ring__and__Field_Osemiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(1519,plain,
class_Ring__and__Field_Osemiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(82,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(1255,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)],[82]) ).
thf(258,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(1676,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)],[258]) ).
thf(186,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(1502,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)],[186]) ).
thf(254,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(1666,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)],[254]) ).
thf(178,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(1487,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)],[178]) ).
thf(819,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(2969,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)],[819]) ).
thf(663,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(2606,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
thf(1370,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_Suc @ A ) ) @ B )
= ( c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(827,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(2986,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(630,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Ovimage @ B @ C @ A @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ ( c_Set_Oimage @ B @ E @ A @ D ) ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).
thf(2528,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Ovimage @ B @ C @ A @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ ( c_Set_Oimage @ B @ E @ A @ D ) ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(400,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(2015,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
thf(1274,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(691,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(2673,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(511,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(2264,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)],[511]) ).
thf(578,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( c_Set_Oinsert @ C @ D @ B ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ D ) ) )
| ( hBOOL @ ( c_in @ C @ D @ B ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__insert_0) ).
thf(2409,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( c_Set_Oinsert @ C @ D @ B ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ D ) ) )
| ( hBOOL @ ( c_in @ C @ D @ B ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
thf(1387,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(352,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
thf(1900,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(278,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).
thf(1723,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(718,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(2733,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)],[718]) ).
thf(749,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(2805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(5,negated_conjecture,
! [A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ ( hAPP @ v_P @ A ) ) @ ( hAPP @ v_c0 @ A ) ) @ ( hAPP @ v_Q @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ t_b )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ ( hAPP @ v_P_H @ A ) ) @ ( hAPP @ v_c0 @ A ) ) @ ( hAPP @ v_Q_H @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ t_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(1042,plain,
! [A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ ( hAPP @ v_P @ A ) ) @ ( hAPP @ v_c0 @ A ) ) @ ( hAPP @ v_Q @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ t_b )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ ( hAPP @ v_P_H @ A ) ) @ ( hAPP @ v_c0 @ A ) ) @ ( hAPP @ v_Q_H @ A ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ t_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(636,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(2541,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(517,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(2277,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)],[517]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
thf(1355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(1580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(941,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBS @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
thf(3239,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBS @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(863,axiom,
! [B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty_0) ).
thf(3069,plain,
! [B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(938,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(3233,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(806,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(2937,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)],[806]) ).
thf(903,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ B )
= B )
| ~ ( c_OrderedGroup_Oab__semigroup__idem__mult @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Omult__idem_0) ).
thf(3154,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ B )
= B )
| ~ ( c_OrderedGroup_Oab__semigroup__idem__mult @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(894,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ D @ C @ A ) ) @ ( c_Set_Oimage @ B @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(3134,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ D @ C @ A ) ) @ ( c_Set_Oimage @ B @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(451,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(2132,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(786,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(2890,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)],[786]) ).
thf(1038,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).
thf(3471,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(961,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(3286,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(211,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
thf(1560,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(229,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(1602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
thf(1920,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(896,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Set_Oinsert @ A @ D @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(3137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Set_Oinsert @ A @ D @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
thf(1178,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(481,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D @ C )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__the__inv__into_0) ).
thf(2200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D @ C )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(473,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(2179,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)],[473]) ).
thf(899,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(3144,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)],[899]) ).
thf(250,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(1656,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)],[250]) ).
thf(16,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(1079,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)],[16]) ).
thf(143,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D ) ) @ E ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
thf(1407,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D ) ) @ E ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(494,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).
thf(2228,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
thf(1573,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(1028,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
| ~ ( c_Lattices_Olower__semilattice @ D @ E @ A @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__absorb2_0) ).
thf(3445,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
| ~ ( c_Lattices_Olower__semilattice @ D @ E @ A @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(959,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ D ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ C @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infI_0) ).
thf(3282,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ D ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ C @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(815,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) @ B )
= ( c_Set_Oinsert @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(2958,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) @ B )
= ( c_Set_Oinsert @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
thf(1423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(971,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) @ ( hAPP @ B @ E ) ) )
| ~ ( hBOOL @ ( c_in @ E @ D @ C ) )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_0) ).
thf(3307,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) @ ( hAPP @ B @ E ) ) )
| ~ ( hBOOL @ ( c_in @ E @ D @ C ) )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(954,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(3271,plain,
class_Lattices_Oupper__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(593,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D )
= ( c_Set_Oinsert @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(2445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D )
= ( c_Set_Oinsert @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(601,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(2464,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(729,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ D ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ C @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__greatest_0) ).
thf(2758,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ D ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ C @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(126,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(1365,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)],[126]) ).
thf(672,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ A @ ( tc_fun @ A @ A ) @ C ) @ D @ C @ A @ A ) @ E @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Osetsum @ B @ E @ C @ A ) ) @ ( c_Finite__Set_Osetsum @ D @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__addf_0) ).
thf(2628,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ A @ ( tc_fun @ A @ A ) @ C ) @ D @ C @ A @ A ) @ E @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Osetsum @ B @ E @ C @ A ) ) @ ( c_Finite__Set_Osetsum @ D @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(690,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ D ) @ C @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).
thf(2670,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ D ) @ C @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(588,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
thf(2433,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(608,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(2477,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(1010,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(3403,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)],[1010]) ).
thf(381,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ E ) )
| ~ ( c_Lattices_Olower__semilattice @ F @ A @ B @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oless__infI1_0) ).
thf(1968,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ E ) )
| ~ ( c_Lattices_Olower__semilattice @ F @ A @ B @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(874,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(3090,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(647,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(2565,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(759,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(2826,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(756,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(2820,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)],[756]) ).
thf(345,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(1888,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
thf(1296,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(322,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).
thf(1836,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(303,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(1787,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)],[303]) ).
thf(845,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I5_J_0) ).
thf(3028,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(855,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff__eq__card_0) ).
thf(3050,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(547,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(2344,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)],[547]) ).
thf(33,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(1128,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)],[33]) ).
thf(614,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(2492,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).
thf(1281,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(722,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(2741,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(847,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Finite__Set_Ofold__graph @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ A @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).
thf(3033,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Finite__Set_Ofold__graph @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ A @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(1012,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ B @ G @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ B @ G @ D @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ G ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_1) ).
thf(3408,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ B @ G @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ B @ G @ D @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ G ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ 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_min__max_Ole__supI_0) ).
thf(1740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ 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)],[285]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__inf__sup_0) ).
thf(1910,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(527,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(2300,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)],[527]) ).
thf(375,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).
thf(1953,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(310,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).
thf(1804,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(788,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( c_Set_Oinsert @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(2895,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( c_Set_Oinsert @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ 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_min__max_Ole__infI_0) ).
thf(1328,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ 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)],[111]) ).
thf(554,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Complete__Lattice_OInf__class_OInf @ B @ A ) ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
thf(2359,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Complete__Lattice_OInf__class_OInf @ B @ A ) ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(714,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ B ) @ C ) @ D )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ E ) @ F ) @ G ) )
| ( C = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
thf(2724,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ B ) @ C ) @ D )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ E ) @ F ) @ G ) )
| ( C = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(868,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) ) @ ( c_Finite__Set_Ocard @ C @ D ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ E @ A @ B @ D ) ) @ C ) )
| ~ ( c_Fun_Oinj__on @ E @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__inj__on__le_0) ).
thf(3078,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) ) @ ( c_Finite__Set_Ocard @ C @ D ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ E @ A @ B @ D ) ) @ C ) )
| ~ ( c_Fun_Oinj__on @ E @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
thf(1755,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(502,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ D @ C ) @ E ) ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ D @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__inf__iff_0) ).
thf(2245,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ D @ C ) @ E ) ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).
thf(1350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(20,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(1089,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)],[20]) ).
thf(202,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__fold__inf_0) ).
thf(1541,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(463,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Suc @ ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ A ) )
= ( c_Finite__Set_Ocard @ B @ A ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__Diff1_0) ).
thf(2157,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Suc @ ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ A ) )
= ( c_Finite__Set_Ocard @ B @ A ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(765,axiom,
! [E: $i,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 ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_0) ).
thf(2840,plain,
! [E: $i,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 ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(38,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(1143,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)],[38]) ).
thf(624,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).
thf(2515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(947,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).
thf(3254,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(328,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D ) ) @ E ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
thf(1851,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D ) ) @ E ) ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
thf(1772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(84,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(1259,plain,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(889,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(3122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(810,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(2946,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(830,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(2990,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)],[830]) ).
thf(651,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ A @ C ) @ D ) @ ( c_Set_Oinsert @ E @ F @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ B @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ A @ C ) @ D ) @ F ) ) )
| ( hBOOL @ ( c_in @ E @ F @ C ) )
| ~ ( c_Finite__Set_Ofinite @ F @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__image__insert_0) ).
thf(2577,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ A @ C ) @ D ) @ ( c_Set_Oinsert @ E @ F @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ B @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ A @ C ) @ D ) @ F ) ) )
| ( hBOOL @ ( c_in @ E @ F @ C ) )
| ~ ( c_Finite__Set_Ofinite @ F @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(1001,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(3381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(11,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(1064,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(708,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
thf(2709,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(382,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(1970,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__join @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__left_0) ).
thf(1227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__join @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(931,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(3218,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(330,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(1856,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)],[330]) ).
thf(621,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 ) @ ( c_Set_Oimage @ A @ B @ C @ C ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
thf(2509,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 ) @ ( c_Set_Oimage @ A @ B @ C @ C ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(879,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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 ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Diff__eq_0) ).
thf(3102,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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 ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(340,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(1878,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(673,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( c_Fun_Othe__inv__into @ B @ A @ C @ D ) @ E ) )
= E )
| ~ ( hBOOL @ ( c_in @ E @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__the__inv__into__f_0) ).
thf(2631,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( c_Fun_Othe__inv__into @ B @ A @ C @ D ) @ E ) )
= E )
| ~ ( hBOOL @ ( c_in @ E @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(859,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(3060,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)],[859]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(1397,plain,
! [B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(181,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(1493,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(46,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(1160,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)],[46]) ).
thf(124,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(1361,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)],[124]) ).
thf(97,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(1292,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)],[97]) ).
thf(645,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(2561,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(582,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(2419,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)],[582]) ).
thf(500,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Osetsum @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) @ B @ tc_nat )
= ( c_Finite__Set_Osetsum @ A @ C @ B @ tc_nat ) )
| ( hBOOL @ ( c_in @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__nat_1) ).
thf(2240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Osetsum @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) @ B @ tc_nat )
= ( c_Finite__Set_Osetsum @ A @ C @ B @ tc_nat ) )
| ( hBOOL @ ( c_in @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).
thf(1214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(160,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(1446,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)],[160]) ).
thf(688,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(2666,plain,
class_Lattices_Olower__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(535,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(2317,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)],[535]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(1082,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(403,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_1) ).
thf(2023,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(834,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ E @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Finite__Set_Osetsum @ B @ D @ E @ A ) ) )
| ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__insert_0) ).
thf(3000,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ E @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Finite__Set_Osetsum @ B @ D @ E @ A ) ) )
| ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(915,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(3179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(876,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) )
= C )
| ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(3094,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) )
= C )
| ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(1461,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1026,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ C @ D @ A ) ) @ ( c_Set_Oimage @ B @ E @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ 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__subset__iff_1) ).
thf(3441,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ C @ D @ A ) ) @ ( c_Set_Oimage @ B @ E @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ 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)],[1026]) ).
thf(533,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) @ ( c_Finite__Set_Osetsum @ B @ E @ C @ A ) ) ) @ ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ C )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un_0) ).
thf(2312,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) @ ( c_Finite__Set_Osetsum @ B @ E @ C @ A ) ) ) @ ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ C )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(268,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).
thf(1700,plain,
class_HOL_Ominus @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(369,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(1937,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(312,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(1810,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)],[312]) ).
thf(470,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_0) ).
thf(2172,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(233,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D )
= E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(1612,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(824,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ C @ D @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I14_J_0) ).
thf(2978,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ C @ D @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(681,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ C ) )
| ~ ( c_Lattices_Olower__semilattice @ D @ E @ A @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__iff__inf_0) ).
thf(2649,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ C ) )
| ~ ( c_Lattices_Olower__semilattice @ D @ E @ A @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(619,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).
thf(2504,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(222,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(1588,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(529,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(2304,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(34,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(1131,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)],[34]) ).
thf(384,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(1974,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(501,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(2243,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)],[501]) ).
thf(552,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(2355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(933,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(3222,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)],[933]) ).
thf(308,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(1799,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)],[308]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).
thf(1947,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(388,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(1984,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)],[388]) ).
thf(752,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D ) )
| ~ ( 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 ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(2813,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D ) )
| ~ ( 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 ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(338,axiom,
class_Lattices_Olower__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(1874,plain,
class_Lattices_Olower__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(774,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 ) @ ( c_Set_Oimage @ C @ D @ E @ B ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
thf(2862,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 ) @ ( c_Set_Oimage @ C @ D @ E @ B ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(274,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(1715,plain,
class_Lattices_Olattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ C ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__insert_0) ).
thf(1979,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ C ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(871,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Osetsum @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) @ B @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_Finite__Set_Osetsum @ A @ C @ B @ tc_nat ) ) @ ( hAPP @ A @ D ) ) )
| ~ ( hBOOL @ ( c_in @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__nat_0) ).
thf(3083,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Osetsum @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) @ B @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_Finite__Set_Osetsum @ A @ C @ B @ tc_nat ) ) @ ( hAPP @ A @ D ) ) )
| ~ ( hBOOL @ ( c_in @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(299,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) )
| ( D
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
thf(1776,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) )
| ( D
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).
thf(1263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
thf(1150,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
thf(1478,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(626,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( hBOOL @ ( c_in @ E @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(2519,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( hBOOL @ ( c_in @ E @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(634,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(2536,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)],[634]) ).
thf(695,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Othe__inv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( hAPP @ B @ D ) )
= D )
| ~ ( 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_the__inv__f__f_0) ).
thf(2681,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Othe__inv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( hAPP @ B @ D ) )
= D )
| ~ ( 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)],[695]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
thf(1530,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(201,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
thf(1539,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(1456,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(612,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
= ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( c_OrderedGroup_Oab__semigroup__idem__mult @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Omult__left__idem_0) ).
thf(2487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
= ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( c_OrderedGroup_Oab__semigroup__idem__mult @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(767,axiom,
class_HOL_Ominus @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
thf(2845,plain,
class_HOL_Ominus @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(990,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(3354,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(568,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_0) ).
thf(2387,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(320,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(1831,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)],[320]) ).
thf(732,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).
thf(2766,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).
thf(2052,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(610,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) )
| ( hBOOL @ ( c_in @ C @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).
thf(2482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) )
| ( hBOOL @ ( c_in @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(702,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(2697,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)],[702]) ).
thf(560,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).
thf(2370,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(930,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(3215,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)],[930]) ).
thf(900,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Nitpick_Ofold__graph_H @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( c_Nitpick_Ofold__graph_H @ A @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ F @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) ) @ E @ F @ G )
| ~ ( hBOOL @ ( c_in @ D @ C @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I2_J_0) ).
thf(3147,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Nitpick_Ofold__graph_H @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( c_Nitpick_Ofold__graph_H @ A @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ F @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) ) @ E @ F @ G )
| ~ ( hBOOL @ ( c_in @ D @ C @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(674,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(2634,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(802,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ A @ C ) @ D ) @ ( c_Set_Oinsert @ E @ F @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ A @ C ) @ D ) @ F ) ) )
| ( hBOOL @ ( c_in @ E @ F @ C ) )
| ~ ( c_Finite__Set_Ofinite @ F @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__image__insert_0) ).
thf(2926,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ A @ C ) @ D ) @ ( c_Set_Oinsert @ E @ F @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ A @ C ) @ D ) @ F ) ) )
| ( hBOOL @ ( c_in @ E @ F @ C ) )
| ~ ( c_Finite__Set_Ofinite @ F @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(483,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(2203,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)],[483]) ).
thf(19,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ( C = E )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(1086,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
| ( C = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(705,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(2702,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(300,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ A )
= ( c_Orderings_Oord__class_Omax @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__max_0) ).
thf(1779,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ A )
= ( c_Orderings_Oord__class_Omax @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(912,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(3173,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(212,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) @ E ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
thf(1563,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) @ E ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(349,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(1895,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)],[349]) ).
thf(544,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( 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 ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__eq_0) ).
thf(2338,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( 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 ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(584,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(2423,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)],[584]) ).
thf(282,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(1732,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)],[282]) ).
thf(1040,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(3476,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)],[1040]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(1333,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(418,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(2057,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
thf(1712,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(326,axiom,
! [A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_OrderedGroup_Oab__semigroup__idem__mult @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__sup_0) ).
thf(1846,plain,
! [A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_OrderedGroup_Oab__semigroup__idem__mult @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(725,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B )
= C )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 @ B @ C @ A ) @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__eqI_0) ).
thf(2748,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B )
= C )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 @ B @ C @ A ) @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) )
| ( ( c_Suc @ A )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(1170,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) )
| ( ( c_Suc @ A )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(817,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).
thf(2963,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(559,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(2368,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)],[559]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(1187,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(797,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
thf(2915,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(591,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Diff__UNIV_0) ).
thf(2440,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(577,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(2408,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)],[577]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).
thf(1663,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(432,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
thf(2089,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(679,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(2645,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)],[679]) ).
thf(832,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(2995,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)],[832]) ).
thf(457,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(2144,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)],[457]) ).
thf(247,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ A )
= ( c_Finite__Set_Ofold1 @ ( c_Orderings_Oord__class_Omax @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__def__raw_0) ).
thf(1648,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ A )
= ( c_Finite__Set_Ofold1 @ ( c_Orderings_Oord__class_Omax @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(693,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ C ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ E @ B @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__le1_0) ).
thf(2677,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ C ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ E @ B @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(570,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(2391,plain,
! [B: $i,A: $i] :
( ( class_HOL_Ouminus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ouminus @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(267,axiom,
! [A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_Lattices_Olower__semilattice @ ( c_COMBC @ ( c_lessequals @ A ) @ A @ A @ tc_bool ) @ ( c_COMBC @ ( c_HOL_Oord__class_Oless @ A ) @ A @ A @ tc_bool ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dual__semilattice_0) ).
thf(1698,plain,
! [A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_Lattices_Olower__semilattice @ ( c_COMBC @ ( c_lessequals @ A ) @ A @ A @ tc_bool ) @ ( c_COMBC @ ( c_HOL_Oord__class_Oless @ A ) @ A @ A @ tc_bool ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(176,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ A )
= ( c_Orderings_Oord__class_Omin @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__min_0) ).
thf(1483,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ A )
= ( c_Orderings_Oord__class_Omin @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(364,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(1927,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)],[364]) ).
thf(950,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(3262,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)],[950]) ).
thf(962,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(3289,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)],[962]) ).
thf(661,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(2602,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)],[661]) ).
thf(628,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).
thf(2524,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(509,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).
thf(2260,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(92,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(1278,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)],[92]) ).
thf(355,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(1906,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)],[355]) ).
thf(80,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(1251,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_minus__add_0) ).
thf(1764,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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)],[294]) ).
thf(892,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ E @ B ) ) @ ( c_Set_Ovimage @ A @ D @ E @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).
thf(3130,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E @ B )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ E @ B ) ) @ ( c_Set_Ovimage @ A @ D @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(516,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Set_Oinsert @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ D @ tc_bool ) ) @ E ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ) @ D ) @ F @ D @ D )
| ( hBOOL @ ( c_in @ C @ E @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ D ) )
| ~ ( c_Finite__Set_Ofold__graph @ A @ C @ E @ F @ D @ D )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__graph__permute__diff_0) ).
thf(2275,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Set_Oinsert @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ D @ tc_bool ) ) @ E ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ) @ D ) @ F @ D @ D )
| ( hBOOL @ ( c_in @ C @ E @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ D ) )
| ~ ( c_Finite__Set_Ofold__graph @ A @ C @ E @ F @ D @ D )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(459,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ B @ ( c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 @ A @ B @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ C ) @ C ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_0) ).
thf(2149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ B @ ( c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 @ A @ B @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ C ) @ C ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(948,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(3257,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(68,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_OrderedGroup_Oab__semigroup__idem__mult @ ( c_Orderings_Oord__class_Omax @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__max_0) ).
thf(1219,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_OrderedGroup_Oab__semigroup__idem__mult @ ( c_Orderings_Oord__class_Omax @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
thf(1747,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(808,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_Finite__Set_Ocard @ B @ A ) ) @ ( c_Finite__Set_Ocard @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__subset_0) ).
thf(2941,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_Finite__Set_Ocard @ B @ A ) ) @ ( c_Finite__Set_Ocard @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
thf(1301,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(226,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(1595,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)],[226]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).
thf(1154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(997,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 ) @ ( c_Set_Oinsert @ D @ C @ A ) ) )
| ( hBOOL @ ( c_in @ D @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(3372,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 ) @ ( c_Set_Oinsert @ D @ C @ A ) ) )
| ( hBOOL @ ( c_in @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(359,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(1916,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(343,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(1884,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(1125,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(825,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(2981,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)],[825]) ).
thf(236,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(1620,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)],[236]) ).
thf(365,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ B @ E @ D @ F ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ B @ E @ D @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_2) ).
thf(1929,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ B @ E @ D @ F ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ B @ E @ D @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(955,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Osetsum @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_Finite__Set_Osetsum @ A @ C @ B @ tc_nat ) ) @ ( c_Finite__Set_Osetsum @ A @ D @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff__nat_0) ).
thf(3272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Osetsum @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ tc_nat )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_Finite__Set_Osetsum @ A @ C @ B @ tc_nat ) ) @ ( c_Finite__Set_Osetsum @ A @ D @ B @ tc_nat ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(199,axiom,
! [D: $i,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 ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).
thf(1535,plain,
! [D: $i,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 ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(711,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(2716,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(380,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ F ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
thf(1965,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ F ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(701,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).
thf(2695,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(452,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBS @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).
thf(2134,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBS @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(929,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(3213,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)],[929]) ).
thf(864,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ A @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) )
| ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__le__fold__sup_0) ).
thf(3070,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 ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ A @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) )
| ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(715,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(2727,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(939,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
thf(3234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(773,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) @ ( c_Finite__Set_Osetsum @ B @ E @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ D ) )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff_0) ).
thf(2859,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) @ ( c_Finite__Set_Osetsum @ B @ E @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ D ) )
| ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(234,axiom,
! [D: $i,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 ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
thf(1615,plain,
! [D: $i,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 ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(302,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(1784,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)],[302]) ).
thf(136,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(1389,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)],[136]) ).
thf(684,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D ) ) @ ( c_Finite__Set_Ocard @ B @ C ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image__le_0) ).
thf(2657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D ) ) @ ( c_Finite__Set_Ocard @ B @ C ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(769,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ( B = C )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(2849,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ( B = C )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(571,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).
thf(2393,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(872,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 @ A @ C @ D @ E ) @ ( c_Set_Oimage @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__transfer_0) ).
thf(3086,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 @ A @ C @ D @ E ) @ ( c_Set_Oimage @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(952,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ A ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ B @ A ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).
thf(3266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ A ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ B @ A ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(648,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__empty_0) ).
thf(2568,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(306,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 ) @ ( c_Suc @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(1795,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 ) @ ( c_Suc @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(269,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(1701,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)],[269]) ).
thf(573,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(2398,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)],[573]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).
thf(1520,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(754,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Ovimage @ B @ C @ A @ D ) ) @ ( c_Set_Ovimage @ B @ E @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
thf(2817,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Ovimage @ B @ C @ A @ D ) ) @ ( c_Set_Ovimage @ B @ E @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(152,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(1428,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)],[152]) ).
thf(255,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) @ E ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
thf(1669,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) @ E ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(887,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(3118,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)],[887]) ).
thf(406,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ A @ B @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__empty_0) ).
thf(2029,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ A @ B @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(720,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(2738,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)],[720]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_minus__add__distrib_0) ).
thf(1635,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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)],[242]) ).
thf(393,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ C ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__insert__idem_0) ).
thf(1997,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ C ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(970,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Set_Oimage @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ E ) @ C @ D )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
thf(3304,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Set_Oimage @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ E ) @ C @ D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(968,axiom,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(3302,plain,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(536,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(2319,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)],[536]) ).
thf(911,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ C ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__insert_0) ).
thf(3170,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ C ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(271,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(1707,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(524,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(2293,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(89,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ E ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__atLeastAtMost_0) ).
thf(1271,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ E ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(531,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__image @ A @ B @ C @ D )
= ( c_Finite__Set_Ofold @ ( c_COMBB @ A @ B @ C @ ( tc_fun @ C @ C ) @ D ) @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__image__def_0) ).
thf(2308,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__image @ A @ B @ C @ D )
= ( c_Finite__Set_Ofold @ ( c_COMBB @ A @ B @ C @ ( tc_fun @ C @ C ) @ D ) @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(867,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(3077,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)],[867]) ).
thf(927,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ( ( c_Finite__Set_Osetsum @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Osetsum @ E @ C @ B @ A ) ) @ ( c_Finite__Set_Osetsum @ E @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un__disjoint_0) ).
thf(3208,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ( ( c_Finite__Set_Osetsum @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Osetsum @ E @ C @ B @ A ) ) @ ( c_Finite__Set_Osetsum @ E @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(334,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 ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(1865,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 ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(1058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(26,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(1107,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)],[26]) ).
thf(592,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ A @ B @ B ) @ C ) @ ( c_Set_Oinsert @ D @ E @ B ) )
= ( hAPP @ ( hAPP @ A @ D ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ A @ B @ B ) @ C ) @ E ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B )
| ~ ( c_Lattices_Olower__semilattice @ F @ G @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ofold__inf__insert_0) ).
thf(2442,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ A @ B @ B ) @ C ) @ ( c_Set_Oinsert @ D @ E @ B ) )
= ( hAPP @ ( hAPP @ A @ D ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ A @ B @ B ) @ C ) @ E ) ) )
| ~ ( c_Finite__Set_Ofinite @ E @ B )
| ~ ( c_Lattices_Olower__semilattice @ F @ G @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(727,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(2753,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)],[727]) ).
thf(417,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ ( c_Set_Oinsert @ C @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) @ A @ A )
| ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ C @ D @ E @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__insert__swap_0) ).
thf(2055,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ ( c_Set_Oinsert @ C @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) @ A @ A )
| ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ C @ D @ E @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(1092,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(598,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(2457,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)],[598]) ).
thf(350,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(1897,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(643,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(2557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(243,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ D ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
thf(1638,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ D ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
thf(1224,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(58,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(1194,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)],[58]) ).
thf(694,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(2679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(946,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
thf(3251,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
thf(2097,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(814,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty_0) ).
thf(2955,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(1037,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ C @ D @ A ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I20_J_0) ).
thf(3468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ C @ D @ A ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(444,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(2116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(31,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(1122,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)],[31]) ).
thf(480,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ A @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ A @ A ) @ B ) @ D ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__sup__insert_0) ).
thf(2197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ A @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ A @ A ) @ B ) @ D ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(428,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 ) ) @ ( c_Set_Oimage @ E @ B @ A @ D ) ) @ ( c_Set_Oimage @ E @ C @ A @ D ) ) )
| ~ ( 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(2079,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 ) ) @ ( c_Set_Oimage @ E @ B @ A @ D ) ) @ ( c_Set_Oimage @ E @ C @ A @ D ) ) )
| ~ ( 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)],[428]) ).
thf(555,axiom,
class_Lattices_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(2361,plain,
class_Lattices_Odistrib__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).
thf(1209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(713,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(2721,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)],[713]) ).
thf(989,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(3352,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(635,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(2538,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(1853,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(430,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(2084,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)],[430]) ).
thf(488,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_HOL_Otimes__class_Otimes @ A ) @ A @ A ) @ B ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__eq__fold__idem_0) ).
thf(2214,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_HOL_Otimes__class_Otimes @ A ) @ A @ A ) @ B ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(580,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(2415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(828,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(2987,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(223,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
thf(1589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(520,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(2284,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)],[520]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C @ A ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ D @ C @ A ) ) ) )
| ~ ( 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(1933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C @ A ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ D @ C @ A ) ) ) )
| ~ ( 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)],[367]) ).
thf(922,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(3197,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)],[922]) ).
thf(1,negated_conjecture,
c_Finite__Set_Ofinite @ v_F @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(1043,plain,
c_Finite__Set_Ofinite @ v_F @ t_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(772,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 @ ( hAPP @ A @ B ) @ A @ B @ C @ D )
!= B )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ C )
| ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_3) ).
thf(2856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 @ ( hAPP @ A @ B ) @ A @ B @ C @ D )
!= B )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ C )
| ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(748,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B )
= C )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 @ B @ C @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__eqI_1) ).
thf(2802,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B )
= C )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 @ B @ C @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(564,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq1_1) ).
thf(2378,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(916,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(3182,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)],[916]) ).
thf(861,axiom,
! [D: $i,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 ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(3066,plain,
! [D: $i,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 ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(216,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(1571,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(778,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D @ C )
= A )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__onto_0) ).
thf(2871,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D @ C )
= A )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
thf(1376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(758,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ A ) ) @ ( c_Finite__Set_Ocard @ B @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__less_0) ).
thf(2824,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ A ) ) @ ( c_Finite__Set_Ocard @ B @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(474,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(2182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(404,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_Set_Oinsert @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ A ) @ E @ A @ A )
| ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) )
| ~ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ E @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__graph__permute__diff_0) ).
thf(2025,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_Set_Oinsert @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ A ) @ E @ A @ A )
| ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) )
| ~ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ E @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(857,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(3055,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(671,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(2625,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)],[671]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ C ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__antimono_0) ).
thf(2111,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ C ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(240,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(1630,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(920,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ C @ D @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I16_J_0) ).
thf(3192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ C @ D @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(118,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(1344,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)],[118]) ).
thf(132,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(1381,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)],[132]) ).
thf(822,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(2974,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(316,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D )
= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
thf(1820,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D )
= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(263,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(1688,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)],[263]) ).
thf(739,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A ) @ D ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__fold1__iff_0) ).
thf(2780,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A ) @ D ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(513,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ B ) @ C ) @ D )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ E ) @ F ) @ G ) )
| ( D = G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
thf(2267,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ B ) @ C ) @ D )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ E ) @ F ) @ G ) )
| ( D = G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(908,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(3165,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)],[908]) ).
thf(333,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__meet @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).
thf(1862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__meet @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(323,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(1838,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(110,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(1325,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)],[110]) ).
thf(741,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ A @ B @ D @ C ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) ) @ C ) @ ( c_COMBK @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ A @ B @ D @ C ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_escape_1) ).
thf(2785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ A @ B @ D @ C ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) ) @ C ) @ ( c_COMBK @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ A @ B @ D @ C ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(657,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(2593,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)],[657]) ).
thf(836,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(3006,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)],[836]) ).
thf(966,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ B @ C @ C ) @ D ) @ E ) ) @ ( hAPP @ ( hAPP @ B @ F ) @ D ) ) )
| ~ ( hBOOL @ ( c_in @ F @ E @ C ) )
| ~ ( c_Finite__Set_Ofinite @ E @ C )
| ~ ( c_Lattices_Olower__semilattice @ A @ G @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ofold__inf__le__inf_0) ).
thf(3298,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ B @ C @ C ) @ D ) @ E ) ) @ ( hAPP @ ( hAPP @ B @ F ) @ D ) ) )
| ~ ( hBOOL @ ( c_in @ F @ E @ C ) )
| ~ ( c_Finite__Set_Ofinite @ E @ C )
| ~ ( c_Lattices_Olower__semilattice @ A @ G @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(779,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(2874,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)],[779]) ).
thf(209,axiom,
! [D: $i,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 ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
thf(1556,plain,
! [D: $i,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 ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(522,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(2289,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)],[522]) ).
thf(680,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ A @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_escape_0) ).
thf(2647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ A @ B @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(505,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(2252,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)],[505]) ).
thf(687,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(2664,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)],[687]) ).
thf(766,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
!= B )
| ~ ( c_Lattices_Olower__semilattice @ D @ E @ A @ F )
| ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__iff__inf_1) ).
thf(2842,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
!= B )
| ~ ( c_Lattices_Olower__semilattice @ D @ E @ A @ F )
| ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(1061,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(734,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(2770,plain,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(550,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( c_in @ D @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
thf(2350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( c_in @ D @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(487,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(2212,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)],[487]) ).
thf(763,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ C ) ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ D ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( c_OrderedGroup_Oab__semigroup__idem__mult @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Ofold1__Un2_0) ).
thf(2835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ C ) ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ D ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( c_OrderedGroup_Oab__semigroup__idem__mult @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(245,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ B ) ) @ C ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
thf(1643,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ B ) ) @ C ) ) @ E ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(454,axiom,
! [E: $i,D: $i,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 @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_3) ).
thf(2139,plain,
! [E: $i,D: $i,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 @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(52,axiom,
! [D: $i,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 ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ D ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
thf(1176,plain,
! [D: $i,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 ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ D ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(804,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ C ) ) )
| ( hBOOL @ ( c_in @ B @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__insert_0) ).
thf(2931,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ C ) ) )
| ( hBOOL @ ( c_in @ B @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(155,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(1435,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)],[155]) ).
thf(972,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ ( hAPP @ ( hAPP @ A @ C ) @ F ) @ E @ G )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ D @ F @ E @ G )
| ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).
thf(3310,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ ( hAPP @ ( hAPP @ A @ C ) @ F ) @ E @ G )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ D @ F @ E @ G )
| ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(438,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(2101,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)],[438]) ).
thf(914,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(3178,plain,
class_HOL_Oord @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(462,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(2156,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)],[462]) ).
thf(485,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
thf(2207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(700,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(2693,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)],[700]) ).
thf(620,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A @ A ) @ B ) @ D ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__inf__insert_0) ).
thf(2506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A @ A ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A @ A ) @ B ) @ D ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(60,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(1198,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)],[60]) ).
thf(324,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(1841,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(1020,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_HOL_Oplus__class_Oplus @ A ) @ A @ A ) @ B ) @ C ) )
| ( hBOOL @ ( c_in @ B @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__eq__fold_0) ).
thf(3423,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_HOL_Oplus__class_Oplus @ A ) @ A @ A ) @ B ) @ C ) )
| ( hBOOL @ ( c_in @ B @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(6,negated_conjecture,
( ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ v_P @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ t_a ) @ v_c0 @ t_a @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ v_Q @ t_a @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ v_F @ t_a @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ t_b )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ v_P_H @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ t_a ) @ v_c0 @ t_a @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ v_Q_H @ t_a @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ v_F @ t_a @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ t_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(1044,plain,
( ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ v_P @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ t_a ) @ v_c0 @ t_a @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ v_Q @ t_a @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ v_F @ t_a @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ t_b )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ v_P_H @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ t_a ) @ v_c0 @ t_a @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) ) @ v_Q_H @ t_a @ ( tc_fun @ t_b @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ v_F @ t_a @ ( tc_Hoare__Mirabelle_Otriple @ t_b ) ) @ t_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(640,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(2550,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Suc @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(1245,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ ( c_Suc @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(882,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).
thf(3110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(431,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(2086,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(905,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(3159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(422,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(2064,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)],[422]) ).
thf(942,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).
thf(3241,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(28,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(1113,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)],[28]) ).
thf(746,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(2797,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)],[746]) ).
thf(978,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
thf(3325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(898,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(3142,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)],[898]) ).
thf(424,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).
thf(2069,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(776,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(2867,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)],[776]) ).
thf(813,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(2952,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(666,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq1_0) ).
thf(2614,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(292,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(1758,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)],[292]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
thf(1203,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(409,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ B ) )
| ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).
thf(2037,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ B ) )
| ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(497,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ( hBOOL @ ( c_in @ D @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(2234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ( hBOOL @ ( c_in @ D @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(1134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oidom @ A )
| ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(595,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ 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__Diff__cancel_0) ).
thf(2449,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(116,axiom,
! [D: $i,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 ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
thf(1340,plain,
! [D: $i,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 ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(1032,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ A @ B @ C @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
= E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__image__empty_0) ).
thf(3455,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ A @ B @ C @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
= E ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(790,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
thf(2899,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
thf(1181,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(1551,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(146,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ 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_min__max_Osup__least_0) ).
thf(1413,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ 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)],[146]) ).
thf(15,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(1076,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)],[15]) ).
thf(846,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(3031,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)],[846]) ).
thf(220,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(1583,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)],[220]) ).
thf(1007,axiom,
! [E: $i,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 ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).
thf(3395,plain,
! [E: $i,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 ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(926,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ D @ tc_bool ) ) @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).
thf(3206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ D @ tc_bool ) ) @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(604,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(2471,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(682,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ B ) @ C ) @ D )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ E ) @ F ) @ G ) )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
thf(2652,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ B ) @ C ) @ D )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A ) @ E ) @ F ) @ G ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(964,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(3293,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)],[964]) ).
thf(906,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(3161,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)],[906]) ).
thf(354,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(1905,plain,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(149,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(1420,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)],[149]) ).
thf(781,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(2878,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)],[781]) ).
thf(261,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(1684,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(854,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_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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_Diff__Int__distrib2_0) ).
thf(3048,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_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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)],[854]) ).
thf(696,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).
thf(2684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(482,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(2202,plain,
class_Lattices_Obounded__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(542,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 ) ) @ ( c_Set_Oimage @ E @ B @ A @ D ) ) @ ( c_Set_Oimage @ E @ C @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(2333,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 ) ) @ ( c_Set_Oimage @ E @ B @ A @ D ) ) @ ( c_Set_Oimage @ E @ C @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(39,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(1145,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)],[39]) ).
thf(768,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(2846,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(507,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(2256,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)],[507]) ).
thf(957,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(3278,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(659,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(2597,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(623,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(2513,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)],[623]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
thf(1547,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1005,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(3391,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)],[1005]) ).
thf(686,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
!= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ( c_Fun_Oinj__on @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__card__imp__inj__on_0) ).
thf(2661,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
!= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ( c_Fun_Oinj__on @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(456,axiom,
! [C: $i,B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ c_Com_Ocom_OSKIP ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
thf(2143,plain,
! [C: $i,B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ c_Com_Ocom_OSKIP ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(290,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(1753,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(783,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
| ~ ( c_Lattices_Olower__semilattice @ E @ F @ A @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__assoc_0) ).
thf(2882,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
| ~ ( c_Lattices_Olower__semilattice @ E @ F @ A @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(761,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(2831,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(296,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(1770,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)],[296]) ).
thf(999,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_0) ).
thf(3376,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(974,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) )
| ( hBOOL @ ( c_in @ C @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).
thf(3315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) )
| ( hBOOL @ ( c_in @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(227,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(1598,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)],[227]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(1070,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(883,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(3112,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)],[883]) ).
thf(232,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(1611,plain,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(563,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ B )
= B )
| ~ ( c_Lattices_Olower__semilattice @ C @ D @ A @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__idem_0) ).
thf(2375,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ B )
= B )
| ~ ( c_Lattices_Olower__semilattice @ C @ D @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(870,axiom,
class_HOL_Ouminus @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).
thf(3082,plain,
class_HOL_Ouminus @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(478,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B )
= C )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 @ B @ C @ A ) ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__eqI_1) ).
thf(2192,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B )
= C )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 @ B @ C @ A ) ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(717,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(2732,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)],[717]) ).
thf(371,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(1941,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)],[371]) ).
thf(81,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ A ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ E ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__atLeastLessThan_0) ).
thf(1252,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ A ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ E ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(936,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).
thf(3228,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(471,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(2175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(1230,plain,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(464,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ D @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ D @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq2_1) ).
thf(2160,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ D @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ D @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(23,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(1098,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)],[23]) ).
thf(785,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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_Diff__cancel_0) ).
thf(2888,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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)],[785]) ).
thf(944,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).
thf(3246,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(1029,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) ) @ ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ) )
| ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__le_0) ).
thf(3448,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) ) @ ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ) )
| ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
thf(2165,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(860,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(3063,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)],[860]) ).
thf(986,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ A @ ( c_Set_Oimage @ A @ B @ C @ D ) @ C @ D )
= B )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).
thf(3344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ A @ ( c_Set_Oimage @ A @ B @ C @ D ) @ C @ D )
= B )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(891,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(3127,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)],[891]) ).
thf(1014,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( c_Finite__Set_Ofold1 @ B @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( c_in @ E @ D @ C ) )
| ~ ( c_Finite__Set_Ofinite @ D @ C )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ofold1__belowI_0) ).
thf(3412,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( c_Finite__Set_Ofold1 @ B @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( c_in @ E @ D @ C ) )
| ~ ( c_Finite__Set_Ofinite @ D @ C )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(851,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).
thf(3041,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(841,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ A @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).
thf(3019,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ A @ B @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(869,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(3080,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)],[869]) ).
thf(304,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(1790,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)],[304]) ).
thf(389,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(1987,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)],[389]) ).
thf(275,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ D ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
thf(1716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ D ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(492,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ F @ E ) @ D ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E )
| ~ ( c_Lattices_Olower__semilattice @ A @ G @ F @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Obelow__fold1__iff_0) ).
thf(2224,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ F @ E ) @ D ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E )
| ~ ( c_Lattices_Olower__semilattice @ A @ G @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(597,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ononempty__iff_2) ).
thf(2454,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(885,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( 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__psubset__trans_0) ).
thf(3114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( 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)],[885]) ).
thf(698,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(2688,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)],[698]) ).
thf(982,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).
thf(3334,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(924,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(3202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(336,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(1869,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)],[336]) ).
thf(490,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ A )
= ( c_Finite__Set_Ocard @ B @ A ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__singleton__if_1) ).
thf(2219,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ A )
= ( c_Finite__Set_Ocard @ B @ A ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(449,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(2128,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)],[449]) ).
thf(18,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(1085,plain,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_OrderedGroup_Oab__semigroup__idem__mult @ A @ B )
| ~ ( c_Lattices_Olower__semilattice @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oab__semigroup__idem__mult__inf_0) ).
thf(1658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_OrderedGroup_Oab__semigroup__idem__mult @ A @ B )
| ~ ( c_Lattices_Olower__semilattice @ C @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(538,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(2322,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(704,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(2701,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(792,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_Set_Oinsert @ C @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ E ) @ A @ A )
| ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ E @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__graph__insert__swap_0) ).
thf(2903,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_Set_Oinsert @ C @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ E ) @ A @ A )
| ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ E @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(638,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(2545,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)],[638]) ).
thf(660,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(2599,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)],[660]) ).
thf(992,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ( hBOOL @ ( c_in @ ( hAPP @ A @ D ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) @ C ) )
| ( ( hAPP @ A @ D )
= ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 @ ( hAPP @ A @ D ) @ A @ D @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_2) ).
thf(3359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ( hBOOL @ ( c_in @ ( hAPP @ A @ D ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) @ C ) )
| ( ( hAPP @ A @ D )
= ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 @ ( hAPP @ A @ D ) @ A @ D @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(412,axiom,
( ( hAPP @ ( c_COMBS @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
= ( hAPP @ ( hAPP @ v_P @ v_R ) @ ( hAPP @ v_Q @ v_R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def__raw_0) ).
thf(2044,plain,
( ( hAPP @ ( c_COMBS @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
= ( hAPP @ ( hAPP @ v_P @ v_R ) @ ( hAPP @ v_Q @ v_R ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(811,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(2948,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)],[811]) ).
thf(881,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(3107,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)],[881]) ).
thf(309,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).
thf(1802,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(934,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(3224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(807,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(2939,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(787,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(2892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(512,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(2266,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(654,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_Orderings_Oord__class_Omin @ A ) @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ D @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__strict__below__iff_2) ).
thf(2584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_Orderings_Oord__class_Omin @ A ) @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ D @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(692,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
| ~ ( c_Fun_Oinj__on @ A @ C @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
thf(2675,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
| ~ ( c_Fun_Oinj__on @ A @ C @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(1404,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(123,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(1358,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)],[123]) ).
thf(503,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__left__commute_0) ).
thf(2247,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ D ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(351,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(1898,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)],[351]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(1257,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(764,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(2838,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(1016,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(3415,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(890,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(3124,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(585,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ D @ C ) @ E ) ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ D @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infE_0) ).
thf(2426,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ D @ C ) @ E ) ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(831,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(2992,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)],[831]) ).
thf(637,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(2543,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)],[637]) ).
thf(991,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(3356,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)],[991]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
thf(1221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(94,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(1284,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)],[94]) ).
thf(823,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(2975,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(518,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ C ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__Un_0) ).
thf(2279,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ C ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(553,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(2357,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)],[553]) ).
thf(376,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(1955,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)],[376]) ).
thf(383,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(1972,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)],[383]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(1052,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(709,axiom,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(2711,plain,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ 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_min__max_Ole__sup__iff_2) ).
thf(1506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ 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)],[188]) ).
thf(1004,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ D ) @ C @ A ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ B @ E @ C @ A )
| ~ ( c_Fun_Oinj__on @ B @ D @ C @ A )
| ( c_Fun_Oinj__on @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).
thf(3388,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ D ) @ C @ A ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ B @ E @ C @ A )
| ~ ( c_Fun_Oinj__on @ B @ D @ C @ A )
| ( c_Fun_Oinj__on @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(187,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(1504,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)],[187]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__def_0) ).
thf(1140,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(622,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(2511,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)],[622]) ).
thf(307,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(1797,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)],[307]) ).
thf(843,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(3024,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(76,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(1240,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)],[76]) ).
thf(235,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(1617,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)],[235]) ).
thf(897,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(3139,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)],[897]) ).
thf(1031,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).
thf(3452,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(875,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ E @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
thf(3092,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ E @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(208,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(1553,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(760,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Set_Oimage @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
thf(2828,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Set_Oimage @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(816,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
thf(2960,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
thf(1517,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(850,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).
thf(3039,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(960,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(3284,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(730,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( 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 ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__Un_0) ).
thf(2760,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( ( 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 ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ( ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(399,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).
thf(2013,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(1041,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( c_Set_Oinsert @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ A ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(3478,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( c_Set_Oinsert @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ A ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1009,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).
thf(3400,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(801,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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_Diff__empty_0) ).
thf(2924,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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)],[801]) ).
thf(360,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ 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_min__max_Ole__inf__iff_2) ).
thf(1918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ 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)],[360]) ).
thf(1033,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(3457,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)],[1033]) ).
thf(107,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(1316,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)],[107]) ).
thf(551,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).
thf(2352,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(262,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(1685,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)],[262]) ).
thf(784,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(2885,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)],[784]) ).
thf(45,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(1157,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)],[45]) ).
thf(321,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
thf(1834,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Suc @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(1913,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Suc @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(532,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(2310,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)],[532]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
thf(1844,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(2347,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
thf(1654,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(145,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
thf(1412,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(665,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff2_1) ).
thf(2611,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(539,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__commute_0) ).
thf(2325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).
thf(1216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(486,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I15_J_0) ).
thf(2209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(723,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(2743,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(613,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
thf(2490,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(476,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).
thf(2187,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(976,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ ( c_Set_Oinsert @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(3320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ ( c_Set_Oinsert @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(799,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(2919,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(546,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(2342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(163,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(1453,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)],[163]) ).
thf(678,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(2643,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)],[678]) ).
thf(744,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D )
= ( c_Set_Oinsert @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ A ) )
| ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(2792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D )
= ( c_Set_Oinsert @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ A ) )
| ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(311,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(1807,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)],[311]) ).
thf(794,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( c_Set_Oinsert @ C @ D @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ A @ B @ B ) @ C ) @ D ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B )
| ~ ( c_OrderedGroup_Oab__semigroup__idem__mult @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Ofold1__eq__fold__idem_0) ).
thf(2907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( c_Set_Oinsert @ C @ D @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ A @ B @ B ) @ C ) @ D ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B )
| ~ ( c_OrderedGroup_Oab__semigroup__idem__mult @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(91,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(1276,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)],[91]) ).
thf(246,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(1646,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)],[246]) ).
thf(707,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(2707,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)],[707]) ).
thf(576,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) )
| ( hBOOL @ ( c_in @ C @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).
thf(2406,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) )
| ( hBOOL @ ( c_in @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(642,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__ac_I1_J_0) ).
thf(2554,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
thf(1508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(1101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(983,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(3336,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)],[983]) ).
thf(932,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(3220,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)],[932]) ).
thf(287,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
thf(1745,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(820,axiom,
class_Orderings_Otop @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
thf(2971,plain,
class_Orderings_Otop @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(835,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(3003,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)],[835]) ).
thf(629,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).
thf(2526,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(829,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ A @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_0) ).
thf(2988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ A @ B @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(134,axiom,
! [C: $i,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
thf(1385,plain,
! [C: $i,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(277,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
thf(1721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(467,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ ( hAPP @ ( hAPP @ A @ B ) @ F ) @ E @ E )
| ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( c_Finite__Set_Ofold__graph @ A @ C @ D @ F @ E @ E )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__graph__insert__swap_0) ).
thf(2167,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ ( hAPP @ ( hAPP @ A @ B ) @ F ) @ E @ E )
| ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( c_Finite__Set_Ofold__graph @ A @ C @ D @ F @ E @ E )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(515,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(2273,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)],[515]) ).
thf(569,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ A @ B @ D @ C @ G @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ A @ B @ D @ C ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ G ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_1) ).
thf(2389,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ A @ B @ D @ C @ G @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ A @ B @ D @ C ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ G ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(173,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
thf(1476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(175,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).
thf(1481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(1002,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ A @ B @ D @ C @ E @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_2) ).
thf(3383,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ A @ B @ D @ C @ E @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(880,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B
= ( c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 @ ( hAPP @ A @ B ) @ A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_1) ).
thf(3104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B
= ( c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 @ ( hAPP @ A @ B ) @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_0) ).
thf(2004,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(664,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(2608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(587,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ A ) ) @ ( c_Finite__Set_Ocard @ B @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__le_0) ).
thf(2431,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ A ) ) @ ( c_Finite__Set_Ocard @ B @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(195,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(1523,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(450,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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 ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(2130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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 ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(981,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) @ B )
= C )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(3331,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) @ B )
= C )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(995,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 ) ) @ ( c_Set_Oinsert @ D @ B @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(3368,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 ) ) @ ( c_Set_Oinsert @ D @ B @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
thf(1558,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(805,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ F ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
thf(2934,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ F ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(460,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ ( c_Set_Oinsert @ B @ D @ A ) )
= ( c_Set_Oinsert @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(2152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ ( c_Set_Oinsert @ B @ D @ A ) )
= ( c_Set_Oinsert @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(510,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(2262,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)],[510]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).
thf(1491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ C ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__mono_0) ).
thf(2081,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B ) ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ C ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(411,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(2041,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)],[411]) ).
thf(104,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(1308,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)],[104]) ).
thf(446,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(2120,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)],[446]) ).
thf(435,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ ( c_Set_Oinsert @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ A ) @ E @ A @ A )
| ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) )
| ~ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ C @ D @ E @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__permute__diff_0) ).
thf(2095,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
| ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ ( c_Set_Oinsert @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) @ A ) @ E @ A @ A )
| ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) )
| ~ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ C @ D @ E @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(534,axiom,
( ( hAPP @ ( c_COMBK @ v_P @ t_a @ t_b ) @ v_Q )
= v_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def__raw_0) ).
thf(2315,plain,
( ( hAPP @ ( c_COMBK @ v_P @ t_a @ t_b ) @ v_Q )
= v_P ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(670,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(2623,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)],[670]) ).
thf(2,negated_conjecture,
~ ( hBOOL @ ( c_in @ v_x @ v_F @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(1045,plain,
~ ( hBOOL @ ( c_in @ v_x @ v_F @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(594,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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_empty__Diff_0) ).
thf(2447,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( 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)],[594]) ).
thf(809,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ E ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ B @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infI1_0) ).
thf(2944,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ E ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ B @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(567,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_0) ).
thf(2384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(606,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(2475,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
thf(1294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(600,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ C ) ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).
thf(2462,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ C ) ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(157,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
thf(1440,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(901,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(3149,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)],[901]) ).
thf(556,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ D @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ D @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq2_0) ).
thf(2362,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ D @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ D @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(465,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(2162,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(495,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(2230,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)],[495]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(1893,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(721,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( c_Com_Ocom_OSemi @ D @ E ) ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ G ) @ E ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ D ) @ G ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comp_0) ).
thf(2739,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ ( c_Com_Ocom_OSemi @ D @ E ) ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ G ) @ E ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B ) @ C ) @ D ) @ G ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(615,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(2494,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(1444,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(1442,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(1018,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(3420,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(583,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(2421,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(298,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).
thf(1774,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).
thf(1725,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(377,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(1957,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)],[377]) ).
thf(259,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(1678,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(633,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(2534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(963,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(3291,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)],[963]) ).
thf(826,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(2983,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)],[826]) ).
thf(655,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
= ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( c_Lattices_Olower__semilattice @ D @ E @ A @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__left__idem_0) ).
thf(2587,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
= ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( c_Lattices_Olower__semilattice @ D @ E @ A @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(238,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(1625,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)],[238]) ).
thf(951,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(3264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(733,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ B )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
thf(2768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ B )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(1000,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ B ) ) )
| ~ ( hBOOL @ ( c_in @ D @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__inf__le__inf_0) ).
thf(3379,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ B ) ) )
| ~ ( hBOOL @ ( c_in @ D @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(29,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(1116,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)],[29]) ).
thf(356,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(1908,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)],[356]) ).
thf(447,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( hAPP @ B @ E ) )
= E )
| ~ ( hBOOL @ ( c_in @ E @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__f__f_0) ).
thf(2123,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( hAPP @ B @ E ) )
= E )
| ~ ( hBOOL @ ( c_in @ E @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(508,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(2258,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)],[508]) ).
thf(528,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(2302,plain,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(625,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 @ ( c_Set_Oimage @ C @ A @ B @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
thf(2517,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 @ ( c_Set_Oimage @ C @ A @ B @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(627,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).
thf(2522,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(878,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ D @ B @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).
thf(3100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ D @ B @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(225,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(1593,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)],[225]) ).
thf(662,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ D ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ C @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__inf__iff_2) ).
thf(2604,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ C @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ D ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ F @ C @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(753,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) @ C @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
thf(2815,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) @ C @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(1303,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).
thf(1148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
thf(1673,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(893,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(3132,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)],[893]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(1248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(675,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(2636,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)],[675]) ).
thf(332,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ D ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(1859,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ D ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(980,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ C ) @ D @ C @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__negf_0) ).
thf(3328,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ ( c_COMBB @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ B @ A @ A @ C ) @ D @ C @ A )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(390,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I21_J_0) ).
thf(1989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(125,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(1363,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)],[125]) ).
thf(182,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(1495,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)],[182]) ).
thf(987,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).
thf(3347,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(724,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).
thf(2746,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(706,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Finite__Set_Ocard @ B @ C ) ) @ ( c_Finite__Set_Ocard @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__seteq_0) ).
thf(2704,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Finite__Set_Ocard @ B @ C ) ) @ ( c_Finite__Set_Ocard @ A @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(581,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(2417,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)],[581]) ).
thf(558,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(2366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(1021,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( c_Set_Oinsert @ C @ D @ B ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ D ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__idem__mult @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Ofold1__insert__idem_0) ).
thf(3426,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( c_Set_Oinsert @ C @ D @ B ) )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ D ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ B )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__idem__mult @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(668,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ B @ E @ D @ F ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ B @ E @ D @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_0) ).
thf(2619,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ B ) @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ B @ E @ D @ F ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ B @ E @ D @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ E ) @ C ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(421,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ C @ D @ A ) ) @ ( c_Set_Oimage @ B @ E @ D @ A ) ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(2063,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ C @ D @ A ) ) @ ( c_Set_Oimage @ B @ E @ D @ A ) ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(740,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(2783,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)],[740]) ).
thf(286,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_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(1742,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_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(726,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(2751,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)],[726]) ).
thf(747,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
thf(2800,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(114,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(1335,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)],[114]) ).
thf(265,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(1693,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)],[265]) ).
thf(796,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(2913,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(433,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(2091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(745,axiom,
! [E: $i,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 ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_2) ).
thf(2795,plain,
! [E: $i,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 ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(1473,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(545,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(2340,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)],[545]) ).
thf(48,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(1165,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)],[48]) ).
thf(943,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(3244,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)],[943]) ).
thf(74,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( c_Suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
thf(1236,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( c_Suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(385,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(1977,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(844,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(3025,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)],[844]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(1152,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(858,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(3057,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(131,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(1378,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(363,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(1925,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)],[363]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
thf(1299,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(985,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Suc @ ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) @ C ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert_0) ).
thf(3341,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Suc @ ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) @ C ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(993,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).
thf(3362,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(751,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_Finite__Set_Ocard @ B @ A ) ) @ ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__subset__Int_0) ).
thf(2810,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_Finite__Set_Ocard @ B @ A ) ) @ ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
thf(1352,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(818,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(2966,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
thf(1268,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Int_Onumber__ring @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(133,axiom,
class_Lattices_Odistrib__lattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(1384,plain,
class_Lattices_Odistrib__lattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(200,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(1537,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ B ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(653,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(2583,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)],[653]) ).
thf(949,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(3259,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(184,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(1500,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).
thf(1923,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(775,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(2864,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)],[775]) ).
thf(341,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
thf(1880,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_Suc @ A ) ) @ B ) ) @ ( c_Suc @ C ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(884,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).
thf(3113,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(353,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(1902,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)],[353]) ).
thf(611,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(2484,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ tc_nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(344,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_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(1885,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_Oplus__class_Oplus @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).
thf(1399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(514,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(2270,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(230,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(1606,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)],[230]) ).
thf(379,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 ) @ ( c_Finite__Set_Osetsum @ B @ C @ D @ A ) ) @ E )
= ( c_Finite__Set_Osetsum @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ A @ ( tc_fun @ A @ A ) @ D ) @ D @ A @ A ) @ E ) @ C @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__left__distrib_0) ).
thf(1962,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 ) @ ( c_Finite__Set_Osetsum @ B @ C @ D @ A ) ) @ E )
= ( c_Finite__Set_Osetsum @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ A @ ( tc_fun @ A @ A ) @ D ) @ D @ A @ A ) @ E ) @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(646,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
thf(2563,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(284,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(1737,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)],[284]) ).
thf(589,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(2436,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)],[589]) ).
thf(1023,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(3432,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)],[1023]) ).
thf(469,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(2170,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)],[469]) ).
thf(440,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff2_0) ).
thf(2106,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(169,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
thf(1468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(965,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBB @ A @ B @ C @ D @ E ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ D )
= ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ C ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__composition_0) ).
thf(3296,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBB @ A @ B @ C @ D @ E ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ D )
= ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ C ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(537,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(2321,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(372,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ E ) ) @ ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ) @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ E @ C @ D ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_H_0) ).
thf(1944,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ E ) ) @ ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ) @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ E @ C @ D ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(127,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(1367,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)],[127]) ).
thf(260,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__meet @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).
thf(1681,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__meet @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
thf(1184,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(426,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I11_J_0) ).
thf(2074,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(699,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(2690,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)],[699]) ).
thf(167,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ 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_min__max_Oinf__greatest_0) ).
thf(1463,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ 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)],[167]) ).
thf(833,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ D ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ E @ B @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__le2_0) ).
thf(2998,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ ( hAPP @ B @ C ) @ D ) ) @ D ) )
| ~ ( c_Lattices_Olower__semilattice @ A @ E @ B @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(213,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(1565,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)],[213]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).
thf(1848,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(419,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(2059,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)],[419]) ).
thf(499,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(2238,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)],[499]) ).
thf(179,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(1490,plain,
class_Orderings_Obot @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(526,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(2297,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(1027,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).
thf(3443,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(923,axiom,
! [E: $i,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 ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_1) ).
thf(3200,plain,
! [E: $i,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 ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(161,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(1449,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__join @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__right_0) ).
thf(1812,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__join @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ 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_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(472,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(2177,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(683,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(2655,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)],[683]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C )
!= C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
thf(1417,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C )
!= C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(735,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_5) ).
thf(2771,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(15775,plain,
$false,
inference(e,[status(thm)],[2822,1718,1823,1995,3167,2921,3397,2559,2331,1818,1110,2250,3021,1322,1586,1501,1168,2295,2306,3053,3008,2109,2031,1633,2778,2072,1767,2412,2876,1237,2787,2595,2499,2480,1982,1950,1549,1750,1211,3072,3317,2808,2395,1073,1544,1728,2114,2380,1437,1200,2077,1290,1882,2776,2659,3417,2590,1401,3460,1569,1939,2099,2282,1591,1793,2854,1533,1173,1486,1426,1671,1608,1137,2686,1310,3135,3365,1735,3338,2141,1872,1233,2459,2901,2146,1458,1497,2195,3017,3120,3429,1867,2184,3175,2476,1260,3414,1761,1342,1640,2580,1196,3236,2020,3466,1475,2819,1623,2869,3370,1095,2348,3350,2972,2046,1243,2763,2548,1782,2227,1391,1576,3088,1046,2010,1935,2400,2067,2136,1265,1628,1287,1709,3195,1430,2735,3046,2755,2501,1511,1826,1313,1992,3043,2571,3248,3204,1055,1409,2328,2916,2039,3275,2698,1660,3116,2667,1330,2217,3410,3280,2897,1191,2466,2126,1545,2713,1147,2929,1815,1875,2533,3268,1892,3463,3374,3385,2169,2403,1514,2049,2552,1319,1704,1890,2373,1347,3312,1931,1568,3014,2730,2852,3231,2007,2222,3322,2027,3393,1373,2469,3163,3473,2880,1828,2034,2335,3152,2017,2950,1415,2616,1465,3075,1450,2451,2236,1858,3438,2291,2254,1960,3300,2437,3068,1526,2002,2103,3226,1600,1104,2833,3189,2190,3421,3036,2530,1119,2371,1394,3157,2286,2639,3327,1433,3211,2154,2718,3406,2205,1696,3184,3435,1651,3097,3450,2910,3303,2473,1691,2574,3169,1306,2364,3186,2118,1338,2047,2232,2641,3011,1206,1470,2093,1067,2496,2621,2790,2905,2382,2061,2773,2000,1047,1730,3037,1163,2428,1519,1255,1676,1502,1666,1487,2969,2606,1370,2986,2528,2015,1274,2673,2264,2409,1387,1900,1723,2733,2805,1042,2541,2277,1355,1580,3239,3069,3233,2937,3154,3134,2132,2890,3471,3286,1560,1602,1920,3137,1178,2200,2179,3144,1656,1079,1407,2228,1573,3445,3282,2958,1423,3307,3271,2445,2464,2758,1365,2628,2670,2433,2477,3403,1968,3090,2565,2826,2820,1888,1296,1836,1787,3028,3050,2344,1128,2492,1281,2741,3033,3408,1740,1910,2300,1953,1804,2895,1328,2359,2724,3078,1755,2245,1350,1089,1541,2157,2840,1143,2515,3254,1851,1772,1259,3122,2946,2990,2577,3381,1064,2709,1970,1227,3218,1856,2509,3102,1878,2631,3060,1397,1493,1160,1361,1292,2561,2419,2240,1214,1446,2666,2317,1082,2023,3000,3179,3094,1461,3441,2312,1700,1937,1810,2172,1612,2978,2649,2504,1588,2304,1131,1974,2243,2355,3222,1799,1947,1984,2813,1874,2862,1715,1979,3083,1776,1263,1150,1478,2519,2536,2681,1530,1539,1456,2487,2845,3354,2387,1831,2766,2052,2482,2697,2370,3215,3147,2634,2926,2203,1086,2702,1779,3173,1563,1895,2338,2423,1732,3476,1333,2057,1712,1846,2748,1170,2963,2368,1187,2915,2440,2408,1663,2089,2645,2995,2144,1648,2677,2391,1698,1483,1927,3262,3289,2602,2524,2260,1278,1906,1251,1764,3130,2275,2149,3257,1219,1747,2941,1301,1595,1154,3372,1916,1884,1125,2981,1620,1929,3272,1535,2716,1965,2695,2134,3213,3070,2727,3234,2859,1615,1784,1389,2657,2849,2393,3086,3266,2568,1795,1701,2398,1520,2817,1428,1669,3118,2029,2738,1635,1997,3304,3302,2319,3170,1707,2293,1271,2308,3077,3208,1865,1058,1107,2442,2753,2055,1092,2457,1897,2557,1638,1224,1194,2679,3251,2097,2955,3468,2116,1122,2197,2079,2361,1209,2721,3352,2538,1853,2084,2214,2415,2987,1589,2284,1933,3197,1043,2856,2802,2378,3182,3066,1571,2871,1376,2824,2182,2025,3055,2625,2111,1630,3192,1344,1381,2974,1820,1688,2780,2267,3165,1862,1838,1325,2785,2593,3006,3298,2874,1556,2289,2647,2252,2664,2842,1061,2770,2350,2212,2835,1643,2139,1176,2931,1435,3310,2101,3178,2156,2207,2693,2506,1198,1841,3423,1044,2550,1245,3110,2086,3159,2064,3241,1113,2797,3325,3142,2069,2867,2952,2614,1758,1203,2037,2234,1134,2449,1340,3455,2899,1181,1551,1413,1076,3031,1583,3395,3206,2471,2652,3293,3161,1905,1420,2878,1684,3048,2684,2202,2333,1145,2846,2256,3278,2597,2513,1547,3391,2661,2143,1753,2882,2831,1770,3376,3315,1598,1070,3112,1611,2375,3082,2192,2732,1941,1252,3228,2175,1230,2160,1098,2888,3246,3448,2165,3063,3344,3127,3412,3041,3019,3080,1790,1987,1716,2224,2454,3114,2688,3334,3202,1869,2219,2128,1085,1658,2322,2701,2903,2545,2599,3359,2044,2948,3107,1802,3224,2939,2892,2266,2584,2675,1404,1358,2247,1898,1257,2838,3415,3124,2426,2992,2543,3356,1221,1284,2975,2279,2357,1955,1972,1052,2711,1506,3388,1504,1140,2511,1797,3024,1240,1617,3139,3452,3092,1553,2828,2960,1517,3039,3284,2760,2013,3478,3400,2924,1918,3457,1316,2352,1685,2885,1157,1834,1913,2310,1844,2347,1654,1412,2611,2325,1216,2209,2743,2490,2187,3320,2919,2342,1453,2643,2792,1807,2907,1276,1646,2707,2406,2554,1508,1101,3336,3220,1745,2971,3003,2526,2988,1385,1721,2167,2273,2389,1476,1481,3383,3104,2004,2608,2431,1523,2130,3331,3368,1558,2934,2152,2262,1491,2081,2041,1308,2120,2095,2315,2623,1045,2447,2944,2384,2475,1294,2462,1440,3149,2362,2162,2230,1893,2739,2494,1444,1442,3420,2421,1774,1725,1957,1678,2534,3291,2983,2587,1625,3264,2768,3379,1116,1908,2123,2258,2302,2517,2522,3100,1593,2604,2815,1303,1148,1673,3132,1248,2636,1859,3328,1989,1363,1495,3347,2746,2704,2417,2366,3426,2619,2063,2783,1742,2751,2800,1335,1693,2913,2091,2795,1473,2340,1165,3244,1236,1977,3025,1152,3057,1378,1925,1299,3341,3362,2810,1352,2966,1268,1384,1537,2583,3259,1500,1923,2864,1880,3113,1902,2484,1885,1399,2270,1606,1962,2563,1737,2436,3432,2170,2106,1468,3296,2321,1944,1367,1681,1184,2074,2690,1463,2998,1565,1848,2059,2238,1490,2297,3443,3200,1449,1812,2177,2655,1417,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWV843-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 19 02:12:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.95/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.71/1.14 % [INFO] Parsing done (261ms).
% 1.71/1.14 % [INFO] Running in sequential loop mode.
% 2.48/1.35 % [INFO] eprover registered as external prover.
% 2.48/1.35 % [INFO] cvc4 registered as external prover.
% 2.48/1.36 % [INFO] Scanning for conjecture ...
% 3.26/1.52 % [INFO] Found a conjecture and 1035 axioms. Running axiom selection ...
% 4.01/1.74 % [INFO] Axiom selection finished. Selected 1035 axioms (removed 0 axioms).
% 4.82/1.97 % [INFO] Problem is propositional (TPTP CNF).
% 5.16/1.99 % [INFO] Type checking passed.
% 5.16/2.00 % [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 ...
% 69.83/19.38 % External prover 'e' found a proof!
% 69.83/19.38 % [INFO] Killing All external provers ...
% 69.83/19.39 % Time passed: 18881ms (effective reasoning time: 18239ms)
% 69.83/19.39 % 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)>
% 69.83/19.40 % Axioms used in derivation (1035): cls_inf__sup__aci_I2_J_0, cls_ab__semigroup__mult_Omult__left__commute_0, cls_atLeastatMost__subset__iff_2, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_add__cancel__end_1, cls_subset__insert_1, cls_Diff__iff_2, cls_Min__insert_0, cls_Compl__subset__Compl__iff_1, cls_bot__fun__eq_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_inj__image__mem__iff_1, cls_top__fun__eq_0, cls_atLeastatMost__psubset__iff_1, cls_inf__sup__absorb_0, clsarity_nat__HOL_Oord, cls_vimage__code_0, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_setsum__diff__nat_0, cls_Diff__cancel_0, cls_min__max_Oinf__commute_0, cls_Int__absorb2_0, cls_minus__le__iff_0, cls_Diff1__fold__graph_0, cls_min__max_Ole__infE_0, cls_eq__add__iff2_1, cls_order__le__less__trans_0, cls_min__max_Oless__infI1_0, cls_sup__max_0, cls_less__diff__iff_1, cls_image__constant_0, cls_Compl__Diff__eq_0, cls_compl__sup_0, cls_Un__Diff_0, cls_com_Osimps_I3_J_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_comm__semiring__class_Odistrib_0, cls_Suc__mono_0, cls_min__add__distrib__left_0, cls_equalityI_0, cls_le__diff__iff_0, cls_insert__inter__insert_0, cls_lower__semilattice_Oinf__left__idem_0, cls_min__max_Osup__inf__distrib1_0, cls_Nat_Odiff__diff__eq_0, cls_sup__ge1_0, cls_ivl__disj__un_I21_J_0, cls_add__less__cancel__left_1, cls_insertE_0, cls_Inf__fold__inf_0, cls_less__fun__def_1, cls_Un__subset__iff_0, cls_Suc__inject_0, cls_ivl__disj__un_I20_J_0, cls_eq__imp__le_0, cls_sup__top__left_0, cls_inj__on__iff__eq__card_0, cls_inj__on__Un_2, cls_setsum__diff_0, cls_COMBC__def_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_range__ex1__eq_0, cls_min__max_Oinf__sup__distrib1_0, cls_the__inv__f__f_0, cls_empty__is__image_1, cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0, cls_image__mono_0, cls_Un__empty__left_0, cls_termination__basic__simps_I5_J_0, cls_le__funD_0, cls_atLeastatMost__psubset__iff_2, cls_fun__upd__image_1, cls_xt1_I12_J_0, cls_ab__semigroup__mult_Ofold1__Un_0, cls_finite__insert_0, cls_Diff__eq_0, cls_Suc__n__not__n_0, cls_min__max_Ole__sup__iff_2, cls_inj__on__image__Int_0, cls_fold1__eq__fold__idem_0, cls_min__max_Oinf__le1_0, cls_square__eq__iff_1, cls_inj__image__eq__iff_0, cls_min__less__iff__conj_0, cls_range__ex1__eq_3, cls_sup__bot__right_0, cls_fold1__insert_0, cls_insert__code_1, cls_fun__upd__apply_1, clsarity_nat__Lattices_Odistrib__lattice, cls_atLeastLessThan__subset__iff_1, cls_Int__atLeastAtMost_0, clsarity_bool__Lattices_Olower__semilattice, cls_finite__vimageI_0, cls_less__antisym_0, cls_inf__sup__aci_I6_J_0, cls_Un__upper1_0, cls_Un__commute_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_image__Int_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_eq__diff__iff_0, cls_card__insert_0, cls_dual__semilattice_0, cls_setsum__Un_0, cls_distrib__sup__le_0, cls_Int__mono_0, cls_linorder__neqE_0, cls_add__strict__right__mono_0, cls_Min__eqI_1, cls_vimage__Diff_0, cls_add__sup__distrib__right_0, cls_le__iff__inf_1, cls_conseq_0, cls_lower__semilattice_Oab__semigroup__idem__mult__inf_0, cls_lower__semilattice_Ole__inf__iff_0, cls_fun__Compl__def_0, cls_lower__semilattice_Oinf__commute_0, clsarity_fun__Orderings_Oorder, cls_finite__Un_2, cls_COMBK__def_0, cls_min__max_Osup__inf__absorb_0, cls_UnCI_1, cls_ivl__disj__un_I22_J_0, cls_minus__add__distrib_0, cls_add__le__cancel__left_1, cls_Int__insert__left_0, cls_triple_Oinject_1, cls_ab__semigroup__idem__mult__inf_0, cls_add__imp__eq_0, cls_min__less__iff__disj_2, cls_the__inv__into__onto_0, cls_mem__def_1, cls_add__le__cancel__right_1, cls_fun__upd__image_0, clsarity_nat__Orderings_Olinorder, cls_Diff__Un_0, cls_setsum__Un__disjoint_0, cls_ab__semigroup__mult_Omult__ac_I1_J_0, cls_Inf__lower_0, cls_insert__absorb_0, cls_empty__iff_0, cls_Min__le_0, cls_sup__le__fold__sup_0, cls_setsum__Un__Int_0, cls_Suc__lessI_0, cls_Int__subset__iff_2, cls_less__Suc__eq_2, cls_atLeastatMost__psubset__iff_3, cls_le__inf__iff_1, cls_fold__graph__imp__finite_0, clsarity_bool__HOL_Ominus, cls_not__less__eq_1, cls_Diff__subset__conv_0, cls_image__vimage__subset_0, cls_inj__on__image__set__diff_0, cls_less__supI1_0, cls_min__less__iff__disj_0, cls_minus__diff__eq_0, cls_Int__Un__distrib2_0, cls_compl__eq__compl__iff_0, cls_inf1E_1, cls_class__ringb_Onoteq__reduce_0, cls_Diff__triv_0, cls_minus__minus_0, cls_insert__iff_1, cls_le__maxI2_0, cls_insert__subset_0, cls_comm__monoid__add_Omult__assoc_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_sup__inf__distrib2_0, cls_inj__on__Un__image__eq__iff_0, cls_add__left__cancel_0, cls_less__minus__iff_0, cls_derivs__insertD_1, cls_fold__graph_H_Ointros_I2_J_0, cls_setsum__diff1__nat_1, cls_min__max_Oinf__sup__distrib2_0, cls_class__ring_Osub__add_0, cls_card__insert__if_0, cls_lower__semilattice_Ole__infI_0, cls_ab__semigroup__mult_Omult__commute_0, cls_card__Diff1__less_0, cls_inf__sup__distrib1_0, cls_vimage__UNIV_0, cls_order__less__trans_0, cls_neg__less__iff__less_1, cls_Int__absorb1_0, cls_conseq12_1, cls_add__cancel__21_1, clsarity_fun__Lattices_Oupper__semilattice, cls_fold__graph_H_Ointros_I1_J_0, cls_inj__image__subset__iff_0, cls_fold__inf__insert_0, cls_lower__semilattice_Oless__infI2_0, cls_le__sup__iff_0, cls_ComplD_0, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_inf__left__commute_0, cls_disjoint__eq__subset__Compl_0, cls_lower__semilattice_Ole__infI1_0, cls_inf__commute_0, cls_inj__image__mem__iff_0, cls_inj__image__Compl__subset_0, cls_mult__less__cancel__right__disj_3, cls_finite__insert_1, cls_diff__eq_0, cls_Compl__partition_0, cls_COMBB__def_0, cls_class__ringb_Oadd__mul__solve_1, cls_vimage__Compl_0, cls_subset__insert__iff_2, cls_Min__Un_0, cls_sup__compl__top_0, cls_fold1__Un2_0, cls_fold1__strict__below__iff_2, clsarity_fun__Orderings_Otop, cls_less__max__iff__disj_2, cls_Min__singleton_0, cls_setsum__insert_0, cls_Comp_0, cls_eq__add__iff1_0, cls_Un__left__commute_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, cls_ab__semigroup__idem__mult_Ofold1__insert__idem_0, cls_less__max__iff__disj_0, cls_hoare__derivs_OSkip_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_setsum__diff1_1, cls_nat__less__cases_0, cls_finite__Int_1, cls_Int__empty__right_0, cls_neg__equal__iff__equal_0, cls_min__max_Oless__infI2_0, cls_diff__diff__cancel_0, cls_COMBC__def__raw_0, cls_ab__semigroup__mult_Ononempty__iff_2, cls_COMBS__def_0, cls_lower__semilattice_Ole__iff__inf_1, clsarity_nat__Ring__and__Field_Osemiring__0, cls_Un__Int__distrib2_0, cls_diff__le__mono2_0, cls_Suc__le__mono_0, cls_not__psubset__empty_0, cls_vimage__insert_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_min__max_Ole__inf__iff_1, 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_atLeastLessThan__empty__iff2_0, cls_le__antisym_0, cls_add__right__mono_0, cls_le__supI_0, cls_inf__eq__neg__sup_0, cls_Un__subset__iff_1, cls_Inf__binary_0, cls_less__add__iff2_0, clsarity_nat__Ring__and__Field_Ocomm__semiring, cls_card__Suc__Diff1_0, cls_psubset__insert__iff_8, cls_ivl__disj__int_I11_J_0, cls_order__eq__refl_0, cls_neg__sup__eq__inf_0, cls_order__le__less_0, cls_rangeI_0, cls_order__less__asym_H_0, cls_inj__on__Un_3, cls_rev__image__eqI_0, cls_linorder__antisym__conv1_0, cls_range__composition_0, cls_fold__image__empty_0, cls_Diff__UNIV_0, cls_fold__inf__le__inf_0, cls_class__semiring_Omul__c_0, cls_le__iff__sup_0, cls_empty__is__image_0, cls_psubset__eq_1, cls_inj__on__insert_0, cls_finite__range__imageI_0, cls_fold1__eq__fold_0, clsarity_fun__Orderings_Obot, cls_card__seteq_0, cls_f__the__inv__into__f_0, cls_ab__semigroup__idem__mult_Omult__left__idem_0, cls_triple_Oinject_2, cls_le__supE_1, cls_fun__upd__other_0, cls_lower__semilattice_Oinf__assoc_0, cls_linorder__antisym__conv2_0, cls_add__cancel__end_0, cls_the__inv__into__into_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_comm__monoid__add_Ofold__graph__insert__swap_0, cls_minus__less__iff_1, cls_sup__eq__neg__inf_0, cls_fold1__below__iff_2, cls_conseq1_1, cls_Un__absorb2_0, cls_linorder__neqE__nat_0, cls_psubset__trans_0, cls_inf__sup__aci_I8_J_0, cls_lower__semilattice_Ole__inf__iff_2, cls_min__max_Ole__infE_1, cls_Un__empty__right_0, cls_ivl__disj__un_I5_J_0, cls_insert__ident_0, cls_image__constant__conv_1, cls_vimageI_0, cls_Suc__leI_0, cls_Un__UNIV__right_0, cls_psubset__insert__iff_5, cls_finite__Int_0, cls_atLeastatMost__subset__iff_3, cls_ab__semigroup__idem__mult_Omult__idem_0, cls_minus__add__cancel_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_less__le__not__le_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_min__max_Odistrib__inf__le_0, cls_xt1_I10_J_0, cls_fold__image__insert_0, cls_sup__eq__bot__eq2_0, cls_hoare__derivs_Ointros_I6_J_0, cls_add__less__cancel__right_1, cls_UnCI_0, cls_Un__upper2_0, cls_conseq_2, cls_Compl__disjoint2_0, cls_not__less__iff__gr__or__eq_0, cls_inf__top__right_0, cls_le__minus__iff_0, cls_lower__semilattice_Oinf__idem_0, cls_add__left__mono_0, cls_le__maxI1_0, cls_fold__image__def_0, cls_Int__insert__right_1, cls_atLeastatMost__psubset__iff_0, cls_diff__Suc__Suc_0, cls_min__max_Ole__supE_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_Max__mono_0, cls_min__max_Osup__least_0, cls_ATP__Linkup_OCOMBC__def_0, cls_range__ex1__eq_2, cls_subset__iff_0, cls_insert__code_2, cls_add__strict__left__mono_0, cls_lower__semilattice_Ole__infE_0, cls_Diff__idemp_0, cls_add__le__less__mono_0, cls_not__less__eq__eq_1, cls_greaterThanAtMost__empty_0, cls_rev__predicate1D_0, cls_subset__Compl__self__eq_1, cls_combine__common__factor_0, cls_inf__eq__top__eq1_0, cls_insert__Diff__single_0, cls_min__max_Ole__sup__iff_1, cls_escape_0, cls_singleton__iff_1, cls_atLeastatMost__empty__iff_1, cls_min__max_Osup__left__idem_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_max__diff__distrib__left_0, cls_finite_0, clsarity_fun__HOL_Oord, cls_Compl__Un_0, cls_greaterThanAtMost__empty__iff_0, cls_subset__empty_0, cls_card__psubset_0, cls_less__add__iff1_0, cls_image__insert_0, cls_min__max_Ole__infI2_0, cls_compl__top__eq_0, cls_ab__semigroup__idem__mult__min_0, cls_inf__absorb2_0, cls_le__minus__iff_1, cls_Compl__disjoint_0, cls_vimage__Un_0, cls_finite__Diff_0, cls_diff__single__insert_0, clsarity_fun__Finite__Set_Ofinite_Ofinite, cls_atLeastatMost__empty__iff2_0, cls_fold__sup__insert_0, cls_diff__minus_0, clsarity_bool__Lattices_Oupper__semilattice, cls_COMBB__def__raw_0, cls_class__semiring_Osemiring__rules_I15_J_0, cls_le__max__iff__disj_1, cls_class__semiring_Oadd__a_0, cls_minus__mult__commute_0, cls_UNIV__not__empty_0, cls_min__max_Ole__iff__inf_1, cls_fold__graph_OinsertI_0, cls_class__ringb_Onoteq__reduce_1, cls_Un__insert__left_0, cls_less__Suc__eq__le_1, cls_inf__sup__ord_I2_J_0, cls_le__add__iff1_1, cls_doubleton__eq__iff_2, cls_Compl__partition2_0, cls_add__eq__inf__sup_0, cls_vimage__singleton__eq_1, cls_subset__insert__iff_3, cls_min__max_Oless__supI1_0, cls_fun__upd__triv_0, cls_add__right__cancel_0, cls_xt1_I8_J_0, cls_diff__def_0, cls_less__add__iff2_1, cls_vimage__const_1, cls_inf__sup__aci_I3_J_0, cls_set__eq__subset_2, cls_Un__mono_0, cls_Int__insert__left_1, cls_insert__subset_1, cls_psubset__insert__iff_4, cls_Min__eqI_0, cls_class__semiring_Osemiring__rules_I16_J_0, cls_Inf__insert_0, cls_mult__left__idem_0, cls_class__semiring_Osemiring__rules_I19_J_0, clsarity_nat__Orderings_Obot, clsarity_nat__Lattices_Olower__semilattice, cls_min__max_Ole__inf__iff_0, cls_inj__image__subset__iff_1, cls_ex__in__conv_0, cls_sup__commute_0, cls_Compl__anti__mono_0, cls_finite__surj_0, cls_min__max_Oinf__assoc_0, cls_class__semiring_Osemiring__rules_I1_J_0, cls_finite__UnI_0, cls_less__infI1_0, cls_lower__semilattice_Oinf__absorb2_0, cls_Compl__UNIV__eq_0, cls_Int__empty__left_0, cls_min__max_Oinf__idem_0, cls_class__semiring_Osemiring__rules_I17_J_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_comm__monoid__add_Omult__commute_0, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_inj__on__the__inv__into_0, cls_min__max_Odistrib__sup__le_0, cls_neg__inf__eq__sup_0, cls_card__Diff__subset__Int_0, cls_min__max_Oinf__left__idem_0, cls_ab__semigroup__idem__mult_Ofold1__eq__fold__idem_0, cls_compl__inf__bot_0, cls_lower__semilattice_Oinf__le2_0, cls_fold__graph_OemptyI_0, clsarity_fun__Lattices_Olattice, cls_min__le__iff__disj_0, cls_lessI_0, cls_le__SucE_0, cls_subset__iff__psubset__eq_0, cls_COMBK__def__raw_0, cls_linorder__linear_0, cls_Un__empty_0, cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0, cls_atLeastLessThan__empty__iff_1, cls_min__max_Osup__idem_0, cls_not__leE_0, cls_class__ringb_Oadd__mul__solve_0, cls_min__max_Ole__supI_0, cls_Un__subset__iff_2, cls_ATP__Linkup_OCOMBB__def_0, cls_add__strict__mono_0, cls_Suc__le__mono_1, cls_setsum__addf_0, cls_Int__assoc_0, cls_conseq12_2, cls_order__antisym_0, cls_add__cancel__21_0, cls_order__trans_0, cls_less__Suc__eq__0__disj_3, cls_psubset__insert__iff_9, cls_max__less__iff__conj_2, cls_inf__le2_0, cls_Compl__eq__Compl__iff_0, cls_strict__below__fold1__iff_0, cls_insert__is__Un_0, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, cls_eq__add__iff1_1, cls_Max__Un_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_card__image__le_0, cls_image__empty_0, cls_finite__UNIV_0, cls_Compl__subset__Compl__iff_0, clsarity_bool__HOL_Ouminus, cls_ab__diff__minus_0, cls_class__semiring_Omul__d_0, cls_subset__trans_0, cls_atLeastAtMost__singleton_0, cls_double__diff_0, cls_com_Osimps_I3_J_1, cls_atLeastatMost__psubset__iff_4, cls_insertI1_0, cls_DiffI_0, cls_psubset__insert__iff_6, cls_lower__semilattice_Ole__infE_1, cls_le__supE_0, cls_subset__Compl__self__eq_0, 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% 69.83/19.40 % No. of inferences in proof: 2083
% 69.83/19.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 18881 ms resp. 18239 ms w/o parsing
% 70.99/19.81 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 70.99/19.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------