TSTP Solution File: SWV875-1 by Leo-III---1.7.7

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV875-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n027.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 12:19:03 EDT 2023

% Result   : Unsatisfiable 14.94s 4.40s
% Output   : Refutation 16.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      : 1250
% Syntax   : Number of formulae    : 2349 ( 395 unt; 152 typ;   0 def)
%            Number of atoms       : 5705 (1288 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 48486 (3194   ~;3508   |;   0   &;41784   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  294 ( 294   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  154 ( 152 usr;  13 con; 0-9 aty)
%            Number of variables   : 7948 (   0   ^;7948   !;   0   ?;7948   :)

% Comments : 
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
    hBOOL: $i > $o ).

thf(hAPP_type,type,
    hAPP: $i > $i > $i ).

thf(c_Natural_Oevalc_type,type,
    c_Natural_Oevalc: $i > $i ).

thf(c_Com_Ocom_OSKIP_type,type,
    c_Com_Ocom_OSKIP: $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 ).

thf(tc_Hoare__Mirabelle_Otriple_type,type,
    tc_Hoare__Mirabelle_Otriple: $i > $i ).

thf(tc_Com_Ostate_type,type,
    tc_Com_Ostate: $i ).

thf(c_Hoare__Mirabelle_Otriple_Otriple_type,type,
    c_Hoare__Mirabelle_Otriple_Otriple: $i > $i > $i > $i > $i ).

thf(c_fequal_type,type,
    c_fequal: $i > $i ).

thf(c_Com_Ocom_OBODY_type,type,
    c_Com_Ocom_OBODY: $i > $i ).

thf(c_Orderings_Obot__class_Obot_type,type,
    c_Orderings_Obot__class_Obot: $i > $i ).

thf(tc_fun_type,type,
    tc_fun: $i > $i > $i ).

thf(tc_bool_type,type,
    tc_bool: $i ).

thf(c_in_type,type,
    c_in: $i > $i ).

thf(tc_Com_Opname_type,type,
    tc_Com_Opname: $i ).

thf(c_Map_Odom_type,type,
    c_Map_Odom: $i > $i > $i > $i ).

thf(c_Com_Obody_type,type,
    c_Com_Obody: $i ).

thf(tc_Com_Ocom_type,type,
    tc_Com_Ocom: $i ).

thf(class_Ring__and__Field_Oordered__semiring__strict_type,type,
    class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).

thf(tc_nat_type,type,
    tc_nat: $i ).

thf(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
    class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).

thf(class_Ring__and__Field_Opordered__semiring_type,type,
    class_Ring__and__Field_Opordered__semiring: $i > $o ).

thf(class_Ring__and__Field_Ocomm__semiring_type,type,
    class_Ring__and__Field_Ocomm__semiring: $i > $o ).

thf(class_Ring__and__Field_Omult__mono_type,type,
    class_Ring__and__Field_Omult__mono: $i > $o ).

thf(class_Ring__and__Field_Osemiring_type,type,
    class_Ring__and__Field_Osemiring: $i > $o ).

thf(class_OrderedGroup_Opordered__comm__monoid__add_type,type,
    class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).

thf(class_OrderedGroup_Omonoid__add_type,type,
    class_OrderedGroup_Omonoid__add: $i > $o ).

thf(class_Ring__and__Field_Oordered__semiring_type,type,
    class_Ring__and__Field_Oordered__semiring: $i > $o ).

thf(class_Ring__and__Field_Omult__zero_type,type,
    class_Ring__and__Field_Omult__zero: $i > $o ).

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(class_Lattices_Olattice_type,type,
    class_Lattices_Olattice: $i > $o ).

thf(c_Finite__Set_Olattice__class_OInf__fin_type,type,
    c_Finite__Set_Olattice__class_OInf__fin: $i > $i ).

thf(c_Finite__Set_Ofold1_type,type,
    c_Finite__Set_Ofold1: $i > $i > $i ).

thf(c_Lattices_Olower__semilattice__class_Oinf_type,type,
    c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).

thf(class_Ring__and__Field_Oordered__idom_type,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

thf(c_HOL_Oord__class_Oless_type,type,
    c_HOL_Oord__class_Oless: $i > $i ).

thf(c_HOL_Ozero__class_Ozero_type,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

thf(c_lessequals_type,type,
    c_lessequals: $i > $i ).

thf(c_HOL_Otimes__class_Otimes_type,type,
    c_HOL_Otimes__class_Otimes: $i > $i ).

thf(class_OrderedGroup_Ogroup__add_type,type,
    class_OrderedGroup_Ogroup__add: $i > $o ).

thf(c_HOL_Ominus__class_Ominus_type,type,
    c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).

thf(class_Ring__and__Field_Oring__no__zero__divisors_type,type,
    class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).

thf(class_Lattices_Olower__semilattice_type,type,
    class_Lattices_Olower__semilattice: $i > $o ).

thf(class_Lattices_Oupper__semilattice_type,type,
    class_Lattices_Oupper__semilattice: $i > $o ).

thf(class_OrderedGroup_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(class_Ring__and__Field_Ono__zero__divisors_type,type,
    class_Ring__and__Field_Ono__zero__divisors: $i > $o ).

thf(c_Orderings_Oord__class_Omax_type,type,
    c_Orderings_Oord__class_Omax: $i > $i ).

thf(class_Ring__and__Field_Oordered__ring__strict_type,type,
    class_Ring__and__Field_Oordered__ring__strict: $i > $o ).

thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
    c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).

thf(c_Map_Omap__le_type,type,
    c_Map_Omap__le: $i > $i > $i > $i > $o ).

thf(c_Fun_Ofun__upd_type,type,
    c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).

thf(c_Option_Ooption_ONone_type,type,
    c_Option_Ooption_ONone: $i > $i ).

thf(tc_Option_Ooption_type,type,
    tc_Option_Ooption: $i > $i ).

thf(c_Option_Ooption_OSome_type,type,
    c_Option_Ooption_OSome: $i > $i ).

thf(c_Finite__Set_Ofinite_type,type,
    c_Finite__Set_Ofinite: $i > $i > $o ).

thf(class_Ring__and__Field_Oordered__semidom_type,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

thf(c_Finite__Set_Ofold_type,type,
    c_Finite__Set_Ofold: $i > $i > $i > $i > $i > $i ).

thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
    class_OrderedGroup_Oab__semigroup__mult: $i > $o ).

thf(c_Finite__Set_Ofun__left__comm_type,type,
    c_Finite__Set_Ofun__left__comm: $i > $i > $i > $o ).

thf(c_COMBK_type,type,
    c_COMBK: $i > $i > $i > $i ).

thf(c_Suc_type,type,
    c_Suc: $i > $i ).

thf(c_Finite__Set_Olinorder__class_OMin_type,type,
    c_Finite__Set_Olinorder__class_OMin: $i > $i ).

thf(c_Map_Omap__add_type,type,
    c_Map_Omap__add: $i > $i > $i > $i > $i ).

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(class_OrderedGroup_Opordered__ab__group__add_type,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

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(class_OrderedGroup_Olordered__ab__group__add_type,type,
    class_OrderedGroup_Olordered__ab__group__add: $i > $o ).

thf(c_SetInterval_Oord__class_OatLeastAtMost_type,type,
    c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).

thf(class_Ring__and__Field_Opordered__ring_type,type,
    class_Ring__and__Field_Opordered__ring: $i > $o ).

thf(c_Finite__Set_Osetsum_type,type,
    c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).

thf(class_Complete__Lattice_Ocomplete__lattice_type,type,
    class_Complete__Lattice_Ocomplete__lattice: $i > $o ).

thf(c_Complete__Lattice_OSup__class_OSup_type,type,
    c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).

thf(class_Lattices_Odistrib__lattice_type,type,
    class_Lattices_Odistrib__lattice: $i > $o ).

thf(c_Finite__Set_Ofold__image_type,type,
    c_Finite__Set_Ofold__image: $i > $i > $i > $i > $i > $i > $i ).

thf(c_Complete__Lattice_Ocomplete__lattice_type,type,
    c_Complete__Lattice_Ocomplete__lattice: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(class_Ring__and__Field_Oring_type,type,
    class_Ring__and__Field_Oring: $i > $o ).

thf(class_OrderedGroup_Oab__group__add_type,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

thf(c_Option_Ooption_Ooption__case_type,type,
    c_Option_Ooption_Ooption__case: $i > $i > $i > $i > $i > $i ).

thf(class_Ring__and__Field_Oordered__comm__semiring__strict_type,type,
    class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).

thf(c_Orderings_Olinorder_type,type,
    c_Orderings_Olinorder: $i > $i > $i > $o ).

thf(c_COMBC_type,type,
    c_COMBC: $i > $i > $i > $i > $i ).

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(class_Ring__and__Field_Omult__mono1_type,type,
    class_Ring__and__Field_Omult__mono1: $i > $o ).

thf(class_OrderedGroup_Oab__semigroup__idem__mult_type,type,
    class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).

thf(c_Com_Ocom_OSemi_type,type,
    c_Com_Ocom_OSemi: $i > $i > $i ).

thf(class_OrderedGroup_Ocancel__semigroup__add_type,type,
    class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).

thf(c_Map_Orestrict__map_type,type,
    c_Map_Orestrict__map: $i > $i > $i > $i > $i ).

thf(t_a_type,type,
    t_a: $i ).

thf(class_Finite__Set_Ofinite_Ofinite_type,type,
    class_Finite__Set_Ofinite_Ofinite: $i > $o ).

thf(class_OrderedGroup_Opordered__ab__semigroup__add_type,type,
    class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).

thf(c_Complete__Lattice_OInf__class_OInf_type,type,
    c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).

thf(c_Lattices_Olower__semilattice_type,type,
    c_Lattices_Olower__semilattice: $i > $i > $i > $i > $o ).

thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
    class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).

thf(c_Finite__Set_Osetprod_type,type,
    c_Finite__Set_Osetprod: $i > $i > $i > $i > $i ).

thf(c_Finite__Set_Olinorder__class_OMax_type,type,
    c_Finite__Set_Olinorder__class_OMax: $i > $i ).

thf(class_OrderedGroup_Olordered__ab__group__add__meet_type,type,
    class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).

thf(class_HOL_Ominus_type,type,
    class_HOL_Ominus: $i > $o ).

thf(c_SetInterval_Oord__class_OlessThan_type,type,
    c_SetInterval_Oord__class_OlessThan: $i > $i > $i ).

thf(c_OrderedGroup_Oab__semigroup__mult_type,type,
    c_OrderedGroup_Oab__semigroup__mult: $i > $i > $o ).

thf(class_OrderedGroup_Oab__semigroup__add_type,type,
    class_OrderedGroup_Oab__semigroup__add: $i > $o ).

thf(c_The_type,type,
    c_The: $i > $i > $i ).

thf(c_Finite__Set_Ofold__graph_type,type,
    c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i ).

thf(class_HOL_Oord_type,type,
    class_HOL_Oord: $i > $o ).

thf(c_Hoare__Mirabelle_OMGT_type,type,
    c_Hoare__Mirabelle_OMGT: $i > $i ).

thf(v_c_type,type,
    v_c: $i ).

thf(c_Set_Ocontents_type,type,
    c_Set_Ocontents: $i > $i > $i ).

thf(class_Lattices_Obounded__lattice_type,type,
    class_Lattices_Obounded__lattice: $i > $o ).

thf(c_Set_Ovimage_type,type,
    c_Set_Ovimage: $i > $i > $i > $i > $i ).

thf(c_Option_Oset_type,type,
    c_Option_Oset: $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(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(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__2_type,type,
    v_sko__Hoare__Mirabelle__Xconseq12__2: $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_Finite__Set_Ocard_type,type,
    c_Finite__Set_Ocard: $i > $i > $i ).

thf(c_Finite__Set_Ofold1Set_type,type,
    c_Finite__Set_Ofold1Set: $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(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1_type,type,
    v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__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(t_b_type,type,
    t_b: $i ).

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(c_Nitpick_Osko__Nitpick__XEx1__def__1__3_type,type,
    c_Nitpick_Osko__Nitpick__XEx1__def__1__3: $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_Map_Osko__Map__Xmap__le__def__1__1_type,type,
    c_Map_Osko__Map__Xmap__le__def__1__1: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1_type,type,
    c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1: $i > $i > $i > $i ).

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__Xab__semigroup__mult__Xfold1__in__1__1_type,type,
    c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2_type,type,
    c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2: $i > $i > $i ).

thf(class_Ring__and__Field_Ofield_type,type,
    class_Ring__and__Field_Ofield: $i > $o ).

thf(c_Option_Othe_type,type,
    c_Option_Othe: $i > $i > $i ).

thf(c_Finite__Set_Olattice_OSup__fin_type,type,
    c_Finite__Set_Olattice_OSup__fin: $i > $i > $i > $i ).

thf(c_Hoare__Mirabelle_Ohoare__valids_type,type,
    c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $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(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_Finite__Set_Olattice_OInf__fin_type,type,
    c_Finite__Set_Olattice_OInf__fin: $i > $i > $i > $i ).

thf(c_Map_Osko__Map__XdomD__1__1_type,type,
    c_Map_Osko__Map__XdomD__1__1: $i > $i > $i > $i > $i ).

thf(574,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/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).

thf(2452,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)],[574]) ).

thf(158,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/sandbox2/benchmark/theBenchmark.p',cls_le__maxI1_0) ).

thf(1469,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)],[158]) ).

thf(986,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).

thf(3399,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).

thf(1001,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OInf__class_OInf @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__insert_0) ).

thf(3434,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OInf__class_OInf @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ 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)],[1001]) ).

thf(777,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/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).

thf(2921,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)],[777]) ).

thf(718,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).

thf(2787,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(585,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ C ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__insert_0) ).

thf(2480,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Otimes__class_Otimes @ A ) @ A ) @ C ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ 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)],[585]) ).

thf(822,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Com_Ocom_OBODY @ D ) @ E @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ D ) @ tc_Com_Ocom ) @ E @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_weak__Body_0) ).

thf(3021,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Com_Ocom_OBODY @ D ) @ E @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ D ) @ tc_Com_Ocom ) @ E @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(98,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).

thf(1322,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(244,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).

thf(1665,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)],[244]) ).

thf(733,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/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

thf(2822,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)],[733]) ).

thf(649,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

thf(2630,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(117,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).

thf(1369,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(762,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__upper_0) ).

thf(2889,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( c_Finite__Set_Ofun__left__comm @ ( c_HOL_Otimes__class_Otimes @ A ) @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_0) ).

thf(1168,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( c_Finite__Set_Ofun__left__comm @ ( c_HOL_Otimes__class_Otimes @ A ) @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(507,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffI_0) ).

thf(2295,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(962,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/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

thf(3345,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)],[962]) ).

thf(526,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageI2_0) ).

thf(2341,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(524,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ( B = D )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(2336,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ( B = D )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(815,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ A ) @ tc_Com_Ocom ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ A ) ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I6_J_0) ).

thf(3008,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ A ) @ tc_Com_Ocom ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ A ) ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(230,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).

thf(1633,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(714,axiom,
    class_Lattices_Olattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(2778,plain,
    class_Lattices_Olattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(413,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).

thf(2072,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(1098,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__absorb2_0) ).

thf(3661,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)],[1098]) ).

thf(196,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

thf(1559,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(5,axiom,
    class_Ring__and__Field_Opordered__semiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).

thf(1105,plain,
    class_Ring__and__Field_Opordered__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(757,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/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__ac_I1_J_0) ).

thf(2876,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)],[757]) ).

thf(62,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).

thf(1237,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(620,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ofold__image @ A @ B @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ F ) @ G @ D )
        = ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ E ) ) @ ( c_Finite__Set_Ofold__image @ A @ B @ C @ F @ G @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ F ) )
      | ~ ( c_Finite__Set_Ofinite @ F @ D )
      | ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__image__insert_0) ).

thf(2559,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ofold__image @ A @ B @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ F ) @ G @ D )
        = ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ E ) ) @ ( c_Finite__Set_Ofold__image @ A @ B @ C @ F @ G @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ F ) )
      | ~ ( c_Finite__Set_Ofinite @ F @ D )
      | ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(1007,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/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_0) ).

thf(3449,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)],[1007]) ).

thf(41,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).

thf(1179,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)],[41]) ).

thf(522,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).

thf(2331,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(308,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).

thf(1818,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(86,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

thf(1295,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)],[86]) ).

thf(365,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D )
      | ~ ( c_Map_Omap__le @ B @ E @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ E @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__le__mapI_0) ).

thf(1956,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D )
      | ~ ( c_Map_Omap__le @ B @ E @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ E @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(191,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/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).

thf(1549,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)],[191]) ).

thf(193,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).

thf(1554,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(10,axiom,
    class_OrderedGroup_Omonoid__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

thf(1110,plain,
    class_OrderedGroup_Omonoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(888,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__insert_0) ).

thf(3172,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(893,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(3185,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(32,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

thf(1158,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(785,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ B @ A ) @ C ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1 @ B @ A ) ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2 @ B @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1 @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2 @ B @ A ) ) @ ( 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 )
      | ~ ( c_OrderedGroup_Oab__semigroup__mult @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__in_0) ).

thf(2940,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ B @ A ) @ C ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1 @ B @ A ) ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2 @ B @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1 @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2 @ B @ A ) ) @ ( 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 )
      | ~ ( c_OrderedGroup_Oab__semigroup__mult @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(951,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ A ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ A ) @ tc_Com_Ocom ) ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OBody_0) ).

thf(3317,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ A ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ A ) @ tc_Com_Ocom ) ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(84,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/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(1290,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)],[84]) ).

thf(481,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Set_Ocontents @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_contents__eq_0) ).

thf(2231,plain,
    ! [B: $i,A: $i] :
      ( ( c_Set_Ocontents @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(543,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Min__eqI_1) ).

thf(2381,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( 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)],[543]) ).

thf(222,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/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).

thf(1618,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)],[222]) ).

thf(858,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ E @ B )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ E @ B ) ) @ ( c_Set_Ovimage @ A @ D @ E @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__insert_0) ).

thf(3098,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ E @ B )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ E @ B ) ) @ ( c_Set_Ovimage @ A @ D @ E @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(270,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).

thf(1728,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(50,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).

thf(1205,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)],[50]) ).

thf(298,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) )
        = ( c_Finite__Set_Ofold @ A @ B @ D @ E @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ E )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ G @ H @ I @ A @ J @ K @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_Osup__Sup__fold__sup_0) ).

thf(1793,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) )
        = ( c_Finite__Set_Ofold @ A @ B @ D @ E @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ E )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ G @ H @ I @ A @ J @ K @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(978,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 @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__le_0) ).

thf(3382,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 @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(323,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).

thf(1855,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)],[323]) ).

thf(48,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

thf(1200,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(1044,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/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

thf(3534,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)],[1044]) ).

thf(351,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).

thf(1924,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(472,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).

thf(2210,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(727,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Map_Odom @ C @ A @ D ) ) )
      | ( ( hAPP @ C @ B )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domIff_1) ).

thf(2808,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Map_Odom @ C @ A @ D ) ) )
      | ( ( hAPP @ C @ B )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(655,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

thf(2644,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(549,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ D ) ) @ ( c_Finite__Set_Osetsum @ B @ E @ C @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__insert_0) ).

thf(2395,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ D ) ) @ ( c_Finite__Set_Osetsum @ B @ E @ C @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(771,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__inf__iff_2) ).

thf(2908,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)],[771]) ).

thf(147,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ B ) @ C @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__0_0) ).

thf(1443,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ ( c_COMBK @ ( c_HOL_Ozero__class_Ozero @ A ) @ A @ B ) @ C @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(713,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/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).

thf(2776,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)],[713]) ).

thf(662,axiom,
    class_Orderings_Obot @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(2659,plain,
    class_Orderings_Obot @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(607,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).

thf(2527,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)],[607]) ).

thf(831,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ c_Com_Ocom_OSKIP @ C @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).

thf(3040,plain,
    ! [C: $i,B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ c_Com_Ocom_OSKIP @ C @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(880,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).

thf(3153,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(632,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__inf__iff_1) ).

thf(2590,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)],[632]) ).

thf(130,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).

thf(1401,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)],[130]) ).

thf(788,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_Finite__Set_Osetprod @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ A )
        = ( c_Finite__Set_Osetprod @ B @ C @ D @ A ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ C ) )
      | ( ( hAPP @ B @ E )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__diff1_1) ).

thf(2947,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_Finite__Set_Osetprod @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ A )
        = ( c_Finite__Set_Osetprod @ B @ C @ D @ A ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ C ) )
      | ( ( hAPP @ B @ E )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(358,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).

thf(1939,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(424,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/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__sup_0) ).

thf(2099,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)],[424]) ).

thf(210,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) @ A @ A )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B @ D @ A @ A ) ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__inf__insert_0) ).

thf(1591,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) @ A @ A )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B @ D @ A @ A ) ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(740,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_HOL_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ A @ A ) @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ C @ D @ A @ A ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph__permute__diff_0) ).

thf(2837,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_HOL_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ A @ A ) @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ C @ D @ A @ A ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(76,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).

thf(1269,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(39,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
       != ( c_Fun_Ofun__upd @ F @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( D = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__eqD1_0) ).

thf(1173,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
       != ( c_Fun_Ofun__upd @ F @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( D = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(165,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( c_Finite__Set_Ofold @ C @ D @ B @ E @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ E )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ C @ I @ J @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__fold__inf_0) ).

thf(1486,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( c_Finite__Set_Ofold @ C @ D @ B @ E @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ E )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ C @ I @ J @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(240,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_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( c_Finite__Set_Ofold @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ C @ A @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__eq__fold__idem_0) ).

thf(1655,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_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( c_Finite__Set_Ofold @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ C @ A @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(836,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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).

thf(3049,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)],[836]) ).

thf(675,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/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

thf(2686,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)],[675]) ).

thf(1080,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

thf(3616,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)],[1080]) ).

thf(583,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(2476,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)],[583]) ).

thf(1063,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(3577,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)],[1063]) ).

thf(534,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_1) ).

thf(2360,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(466,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/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

thf(2195,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)],[466]) ).

thf(819,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(3017,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(296,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).

thf(1788,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(908,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ A @ tc_bool ) ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).

thf(3217,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ A @ tc_bool ) ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).

thf(813,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(3004,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(957,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).

thf(3332,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).

thf(971,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

thf(3367,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(970,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(3365,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(698,axiom,
    ! [A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OBODY @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).

thf(2740,plain,
    ! [A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OBODY @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(834,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Olattice_OSup__fin @ A @ B @ C )
        = ( hAPP @ D @ B ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ E @ D @ F @ G @ H @ A @ I @ J @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__fin__Sup_0) ).

thf(3044,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Olattice_OSup__fin @ A @ B @ C )
        = ( hAPP @ D @ B ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ E @ D @ F @ G @ H @ A @ I @ J @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(273,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(1735,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(461,axiom,
    class_HOL_Oord @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

thf(2184,plain,
    class_HOL_Oord @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(889,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Othe @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the_Osimps_0) ).

thf(3175,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Othe @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(867,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ ( hAPP @ C @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).

thf(3121,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ ( hAPP @ C @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(1020,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(3481,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(1057,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).

thf(3562,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)],[1057]) ).

thf(234,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).

thf(1640,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)],[234]) ).

thf(768,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/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

thf(2901,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)],[768]) ).

thf(949,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_HOL_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ A @ A ) @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ A @ A ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__graph__permute__diff_0) ).

thf(3313,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_HOL_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ A @ A ) @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ A @ A ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).

thf(958,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(3335,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)],[958]) ).

thf(315,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).

thf(1835,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(475,axiom,
    ( ( c_Hoare__Mirabelle_OMGT @ v_c )
    = ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ v_c @ ( c_Natural_Oevalc @ v_c ) @ tc_Com_Ostate ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGT__def__raw_0) ).

thf(2216,plain,
    ( ( c_Hoare__Mirabelle_OMGT @ v_c )
    = ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ v_c @ ( c_Natural_Oevalc @ v_c ) @ tc_Com_Ostate ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(402,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/sandbox2/benchmark/theBenchmark.p',cls_sup__max_0) ).

thf(2046,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)],[402]) ).

thf(805,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(2985,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(391,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).

thf(2020,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(854,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__iff__inf_1) ).

thf(3088,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)],[854]) ).

thf(387,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).

thf(2010,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)],[387]) ).

thf(761,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/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

thf(2886,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)],[761]) ).

thf(417,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/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

thf(2082,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)],[417]) ).

thf(601,axiom,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).

thf(2516,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(529,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

thf(2348,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(1050,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
       != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
      | ( C = D )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(3545,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
       != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
      | ( C = D )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).

thf(691,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/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(2723,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)],[691]) ).

thf(590,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ F @ D ) @ E ) ) )
      | ( E
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ D )
      | ~ ( c_Lattices_Olower__semilattice @ A @ G @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Obelow__fold1__iff_0) ).

thf(2491,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ F @ D ) @ E ) ) )
      | ( E
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ D )
      | ~ ( c_Lattices_Olower__semilattice @ A @ G @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(294,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).

thf(1782,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)],[294]) ).

thf(921,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/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(3249,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)],[921]) ).

thf(146,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/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).

thf(1441,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)],[146]) ).

thf(238,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).

thf(1650,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)],[238]) ).

thf(236,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

thf(1645,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)],[236]) ).

thf(349,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/sandbox2/benchmark/theBenchmark.p',cls_dual__semilattice_0) ).

thf(1921,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)],[349]) ).

thf(124,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/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(1386,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)],[124]) ).

thf(935,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/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(3281,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)],[935]) ).

thf(1014,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( F = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).

thf(3466,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)],[1014]) ).

thf(370,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).

thf(1967,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(411,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/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).

thf(2067,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)],[411]) ).

thf(735,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).

thf(2825,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(440,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).

thf(2136,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)],[440]) ).

thf(342,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B @ F @ D @ E )
      = ( c_Fun_Ofun__upd @ A @ B @ F @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).

thf(1904,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)],[342]) ).

thf(74,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).

thf(1265,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(609,axiom,
    ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
    = ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).

thf(2531,plain,
    ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
    = ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(553,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/sandbox2/benchmark/theBenchmark.p',cls_Min__antimono_0) ).

thf(2405,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)],[553]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).

thf(1623,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(1072,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/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

thf(3597,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)],[1072]) ).

thf(910,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__le2_0) ).

thf(3221,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)],[910]) ).

thf(1092,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/sandbox2/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).

thf(3644,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)],[1092]) ).

thf(696,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(2735,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(87,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).

thf(1298,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)],[87]) ).

thf(666,axiom,
    ! [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_OlessThan @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__int_I4_J_0) ).

thf(2667,plain,
    ! [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_OlessThan @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(525,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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).

thf(2339,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)],[525]) ).

thf(961,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
        = ( c_Finite__Set_Ocard @ C @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert__if_0) ).

thf(3342,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
        = ( c_Finite__Set_Ocard @ C @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).

thf(841,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq2_1) ).

thf(3061,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(685,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(2708,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(94,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).

thf(1313,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)],[94]) ).

thf(621,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Option_Oset @ A @ B )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ( A
        = ( c_Option_Ooption_ONone @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty__eq_0) ).

thf(2562,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Option_Oset @ A @ B )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ( A
        = ( c_Option_Ooption_ONone @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(624,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E )
        = ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__in_0) ).

thf(2571,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E )
        = ( hAPP @ A @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

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/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(2703,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(659,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Com_Ocom_OSemi @ D @ E ) @ F @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ E @ F @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ D @ G @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comp_0) ).

thf(2654,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Com_Ocom_OSemi @ D @ E ) @ F @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ E @ F @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ D @ G @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(227,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/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).

thf(1628,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)],[227]) ).

thf(133,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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

thf(1409,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)],[133]) ).

thf(902,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).

thf(3204,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)],[902]) ).

thf(638,axiom,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(2603,plain,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Oord @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(775,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__commute_0) ).

thf(2916,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)],[775]) ).

thf(898,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ D @ A @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_OleD_0) ).

thf(3195,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ D @ A @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(826,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/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(3029,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)],[826]) ).

thf(399,axiom,
    ! [A: $i] :
      ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_Option_Ooption @ A ) )
      | ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite) ).

thf(2039,plain,
    ! [A: $i] :
      ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_Option_Ooption @ A ) )
      | ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(932,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

thf(3275,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).

thf(329,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/sandbox2/benchmark/theBenchmark.p',cls_le__infI_0) ).

thf(1871,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)],[329]) ).

thf(1062,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ ( c_Option_Ooption_ONone @ D ) @ C @ ( tc_Option_Ooption @ D ) )
        = ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__None__restrict_0) ).

thf(3574,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ ( c_Option_Ooption_ONone @ D ) @ C @ ( tc_Option_Ooption @ D ) )
        = ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).

thf(1081,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/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

thf(3617,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)],[1081]) ).

thf(102,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).

thf(1330,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(570,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/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

thf(2444,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)],[570]) ).

thf(325,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ) @ ( c_Finite__Set_Osetprod @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ B @ D @ C @ A ) ) @ ( c_Finite__Set_Osetprod @ B @ E @ C @ A ) ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C )
      | ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__Un__Int_0) ).

thf(1860,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) ) @ ( c_Finite__Set_Osetprod @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ E ) @ C @ A ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ B @ D @ C @ A ) ) @ ( c_Finite__Set_Osetprod @ B @ E @ C @ A ) ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C )
      | ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(1078,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ A @ C )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).

thf(3612,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ A @ C )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).

thf(1095,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/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(3653,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)],[1095]) ).

thf(175,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/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__inf_0) ).

thf(1511,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)],[175]) ).

thf(498,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__left__commute_0) ).

thf(2274,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)],[498]) ).

thf(672,axiom,
    class_Lattices_Odistrib__lattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

thf(2682,plain,
    class_Lattices_Odistrib__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(312,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/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

thf(1826,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)],[312]) ).

thf(991,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
        = C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).

thf(3410,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
        = C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).

thf(462,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_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A @ D ) ) @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) @ A @ D ) ) @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) @ A @ D ) ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ D )
      | ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__image__Un__Int_0) ).

thf(2185,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_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A @ D ) ) @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) @ A @ D ) ) @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ E ) @ A @ D ) ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ D )
      | ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(151,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/sandbox2/benchmark/theBenchmark.p',cls_less__supI1_0) ).

thf(1455,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)],[151]) ).

thf(314,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

thf(1832,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)],[314]) ).

thf(766,axiom,
    ! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).

thf(2897,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)],[766]) ).

thf(45,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( c_Option_Ooption_ONone @ D ) )
      | ( ( hAPP @ B @ E )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_0) ).

thf(1191,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( c_Option_Ooption_ONone @ D ) )
      | ( ( hAPP @ B @ E )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(380,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).

thf(1992,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(965,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Map_Odom @ B @ C @ D ) ) @ ( c_Map_Odom @ A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__map__add_0) ).

thf(3353,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Map_Odom @ B @ C @ D ) ) @ ( c_Map_Odom @ A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).

thf(154,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).

thf(1462,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(20,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).

thf(1132,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(833,axiom,
    class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).

thf(3043,plain,
    class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(301,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/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).

thf(1800,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)],[301]) ).

thf(687,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(2713,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(974,axiom,
    ! [A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

thf(3374,plain,
    ! [A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).

thf(27,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).

thf(1147,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(259,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).

thf(1704,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(709,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_2) ).

thf(2767,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).

thf(1479,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(694,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(2730,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)],[694]) ).

thf(393,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/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).

thf(2024,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)],[393]) ).

thf(891,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infI1_0) ).

thf(3180,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)],[891]) ).

thf(1074,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).

thf(3602,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( 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)],[1074]) ).

thf(914,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 @ B @ C @ A ) ) @ B ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__eqI_0) ).

thf(3231,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 @ B @ C @ A ) ) @ B ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ ( c_Com_Ocom_OBODY @ A ) @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ A ) ) @ tc_Com_Ostate ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) ) @ tc_Com_Ostate )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ tc_Com_Opname ) @ A ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(1100,plain,
    ! [A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ ( c_Com_Ocom_OBODY @ A ) @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ A ) ) @ tc_Com_Ostate ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) ) @ tc_Com_Ostate )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ tc_Com_Opname ) @ A ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(60,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

thf(1232,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)],[60]) ).

thf(189,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/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(1545,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)],[189]) ).

thf(559,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__eq_1) ).

thf(2420,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(454,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ ( c_Fun_Ofun__upd @ F @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ D @ E )
      | ~ ( c_Map_Omap__le @ A @ F @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__upd_0) ).

thf(2169,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ ( c_Fun_Ofun__upd @ F @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ D @ E )
      | ~ ( c_Map_Omap__le @ A @ F @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(552,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/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

thf(2403,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)],[552]) ).

thf(1090,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/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).

thf(3638,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)],[1090]) ).

thf(66,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).

thf(1247,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)],[66]) ).

thf(403,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/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(2049,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)],[403]) ).

thf(108,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).

thf(1347,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)],[108]) ).

thf(201,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_COMBK @ ( c_Option_Ooption_ONone @ B ) @ ( tc_Option_Ooption @ B ) @ C ) @ C @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__empty_0) ).

thf(1572,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_COMBK @ ( c_Option_Ooption_ONone @ B ) @ ( tc_Option_Ooption @ B ) @ C ) @ C @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(275,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).

thf(1741,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ 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)],[275]) ).

thf(852,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_0) ).

thf(3084,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)],[852]) ).

thf(807,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ofold @ A @ B @ C @ D @ E )
        = F )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ C @ D @ E ) @ F ) )
      | ~ ( c_Finite__Set_Ofun__left__comm @ A @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_Ofold__equality_0) ).

thf(2989,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ofold @ A @ B @ C @ D @ E )
        = F )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ C @ D @ E ) @ F ) )
      | ~ ( c_Finite__Set_Ofun__left__comm @ A @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(1362,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(368,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/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).

thf(1963,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)],[368]) ).

thf(546,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).

thf(2388,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(610,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/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(2533,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)],[610]) ).

thf(386,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( c_Finite__Set_Ofinite @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__def_1) ).

thf(2007,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( c_Finite__Set_Ofinite @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(900,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__singleton_0) ).

thf(3199,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(345,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/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(1911,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)],[345]) ).

thf(1017,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com__det_0) ).

thf(3473,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).

thf(22,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

thf(1136,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)],[22]) ).

thf(324,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

thf(1858,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)],[324]) ).

thf(779,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Ovimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__const_1) ).

thf(2925,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Ovimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(938,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Option_Ooption_Ooption__case @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ C )
      = ( hAPP @ B @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I5_J_0) ).

thf(3290,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Option_Ooption_Ooption__case @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ C )
      = ( hAPP @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).

thf(166,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ B @ A @ C @ D ) @ C @ D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__map__add_0) ).

thf(1489,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ B @ A @ C @ D ) @ C @ D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(789,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ ( c_Suc @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).

thf(2950,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)],[789]) ).

thf(135,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).

thf(1415,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(89,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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).

thf(1302,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)],[89]) ).

thf(721,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ A @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_OleI_0) ).

thf(2794,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ A @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(264,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).

thf(1714,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(394,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Map_Omap__add @ B @ C @ D @ E ) @ D @ E )
      = ( c_Map_Omap__add @ ( c_Map_Omap__add @ A @ B @ D @ E ) @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__assoc_0) ).

thf(2027,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Map_Omap__add @ B @ C @ D @ E ) @ D @ E )
      = ( c_Map_Omap__add @ ( c_Map_Omap__add @ A @ B @ D @ E ) @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(427,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).

thf(2105,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)],[427]) ).

thf(848,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__subset__eq_1) ).

thf(3075,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(420,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).

thf(2090,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)],[420]) ).

thf(984,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/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

thf(3393,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)],[984]) ).

thf(9,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

thf(1109,plain,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(764,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(2893,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(229,axiom,
    class_Ring__and__Field_Omult__mono1 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).

thf(1632,plain,
    class_Ring__and__Field_Omult__mono1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(136,axiom,
    ! [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_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).

thf(1418,plain,
    ! [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_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(483,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/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

thf(2236,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)],[483]) ).

thf(967,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/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(3357,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)],[967]) ).

thf(490,axiom,
    ! [B: $i,A: $i] :
      ( ( c_The @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).

thf(2254,plain,
    ! [B: $i,A: $i] :
      ( ( c_The @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(1060,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/sandbox2/benchmark/theBenchmark.p',cls_fold1__antimono_0) ).

thf(3569,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)],[1060]) ).

thf(249,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_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).

thf(1677,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_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ 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)],[249]) ).

thf(397,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/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).

thf(2034,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)],[397]) ).

thf(120,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

thf(1377,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)],[120]) ).

thf(54,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_OrderedGroup_Oab__semigroup__idem__mult @ ( c_Orderings_Oord__class_Omax @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__max_0) ).

thf(1215,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)],[54]) ).

thf(586,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_0) ).

thf(2483,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(299,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_OrderedGroup_Oab__semigroup__idem__mult @ ( c_Orderings_Oord__class_Omin @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__min_0) ).

thf(1796,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)],[299]) ).

thf(181,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).

thf(1526,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(384,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ B )
      = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_3) ).

thf(2002,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ B )
      = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(426,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).

thf(2103,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)],[426]) ).

thf(912,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/sandbox2/benchmark/theBenchmark.p',cls_Int__greatest_0) ).

thf(3226,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)],[912]) ).

thf(796,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(2965,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)],[796]) ).

thf(318,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 ) )
        = ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B @ C @ A @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__Inf__fold__inf_0) ).

thf(1843,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 ) )
        = ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B @ C @ A @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(407,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
     != ( c_Option_Ooption_ONone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).

thf(2058,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
     != ( c_Option_Ooption_ONone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(537,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageE_0) ).

thf(2367,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(1045,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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

thf(3537,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)],[1045]) ).

thf(738,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq1_1) ).

thf(2833,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(895,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).

thf(3189,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)],[895]) ).

thf(501,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

thf(2281,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(464,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ A @ B @ C @ D )
        = ( c_Map_Omap__add @ B @ A @ C @ D ) )
      | ~ ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_0) ).

thf(2190,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ A @ B @ C @ D )
        = ( c_Map_Omap__add @ B @ A @ C @ D ) )
      | ~ ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(995,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(3421,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(15,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

thf(1119,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(561,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_3) ).

thf(2424,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)],[561]) ).

thf(711,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

thf(2772,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(882,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/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

thf(3157,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)],[882]) ).

thf(485,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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(2242,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)],[485]) ).

thf(503,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Obounded__lattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(2286,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)],[503]) ).

thf(653,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

thf(2639,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(1068,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
        = C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).

thf(3588,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
        = C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).

thf(4,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).

thf(1104,plain,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(1056,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ ( c_Map_Osko__Map__XdomD__1__1 @ B @ A @ D @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Map_Odom @ A @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domD_0) ).

thf(3559,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ ( c_Map_Osko__Map__XdomD__1__1 @ B @ A @ D @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Map_Odom @ A @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).

thf(1076,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
       != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(3606,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
       != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).

thf(905,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

thf(3211,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)],[905]) ).

thf(447,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

thf(2154,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)],[447]) ).

thf(179,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ E @ A @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__Some__iff_2) ).

thf(1521,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ E @ A @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(1026,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(3492,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(689,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
       != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
      | ( B = E )
      | ( B = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(2718,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
       != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
      | ( B = E )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(630,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).

thf(2586,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(760,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ F ) @ ( hAPP @ ( hAPP @ A @ D ) @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ E @ C @ F ) @ G ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).

thf(2884,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ F ) @ ( hAPP @ ( hAPP @ A @ D ) @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ E @ C @ F ) @ G ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(373,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

thf(1975,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)],[373]) ).

thf(1034,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/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_0) ).

thf(3510,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)],[1034]) ).

thf(707,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infE_0) ).

thf(2762,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)],[707]) ).

thf(976,axiom,
    class_HOL_Oord @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(3378,plain,
    class_HOL_Oord @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).

thf(326,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).

thf(1863,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(791,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Orderings_Olinorder @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__less__iff__gr__or__eq_2) ).

thf(2954,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Orderings_Olinorder @ A @ B @ C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(1065,axiom,
    ! [B: $i,A: $i] :
      ( ( c_The @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).

thf(3582,plain,
    ! [B: $i,A: $i] :
      ( ( c_The @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).

thf(1011,axiom,
    ! [A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

thf(3459,plain,
    ! [A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).

thf(944,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ofold @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ F )
        = ( hAPP @ ( hAPP @ A @ D ) @ ( c_Finite__Set_Ofold @ A @ B @ ( c_HOL_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ F ) ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C )
      | ~ ( c_Finite__Set_Ofun__left__comm @ A @ C @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_Ofold__insert__remove_0) ).

thf(3301,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ofold @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ F )
        = ( hAPP @ ( hAPP @ A @ D ) @ ( c_Finite__Set_Ofold @ A @ B @ ( c_HOL_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ F ) ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C )
      | ~ ( c_Finite__Set_Ofun__left__comm @ A @ C @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(582,axiom,
    ! [B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OSemi @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).

thf(2473,plain,
    ! [B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( c_Com_Ocom_OSemi @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(1059,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ B ) @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ C @ D @ B @ B ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set_Ointros_0) ).

thf(3567,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ B ) @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ C @ D @ B @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(625,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) )
        = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__restrict__conv_0) ).

thf(2574,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) )
        = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(656,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Suc @ ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
        = ( c_Finite__Set_Ocard @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Suc__Diff1_0) ).

thf(2646,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Suc @ ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
        = ( c_Finite__Set_Ocard @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(91,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/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).

thf(1306,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)],[91]) ).

thf(451,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

thf(2164,plain,
    class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(433,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).

thf(2118,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)],[433]) ).

thf(105,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/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(1338,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)],[105]) ).

thf(697,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

thf(2737,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)],[697]) ).

thf(654,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_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( 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/sandbox2/benchmark/theBenchmark.p',cls_fold1__insert__idem_0) ).

thf(2641,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_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( 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)],[654]) ).

thf(994,axiom,
    ! [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_Finite__Set_Ofun__left__comm @ A @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_Ofun__left__comm_0) ).

thf(3418,plain,
    ! [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_Finite__Set_Ofun__left__comm @ A @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).

thf(1069,axiom,
    ! [B: $i,A: $i] :
      ( ( c_The @ ( hAPP @ ( c_COMBC @ ( c_fequal @ A ) @ A @ A @ tc_bool ) @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the__eq__trivial_0) ).

thf(3591,plain,
    ! [B: $i,A: $i] :
      ( ( c_The @ ( hAPP @ ( c_COMBC @ ( c_fequal @ A ) @ A @ A @ tc_bool ) @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).

thf(772,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ C @ D @ E ) @ F ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ G ) @ C ) )
      | ~ ( c_Finite__Set_Ofun__left__comm @ A @ D @ E )
      | ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ G ) @ C ) @ D @ E ) @ ( hAPP @ ( hAPP @ A @ G ) @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_Ofold__insert__aux_2) ).

thf(2910,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ C @ D @ E ) @ F ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ G ) @ C ) )
      | ~ ( c_Finite__Set_Ofun__left__comm @ A @ D @ E )
      | ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ G ) @ C ) @ D @ E ) @ ( hAPP @ ( hAPP @ A @ G ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(347,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/sandbox2/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).

thf(1915,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)],[347]) ).

thf(261,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).

thf(1708,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(421,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/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

thf(2093,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)],[421]) ).

thf(93,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/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).

thf(1311,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)],[93]) ).

thf(838,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

thf(3054,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)],[838]) ).

thf(592,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(2496,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(645,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) @ ( c_Finite__Set_Ocard @ A @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Diff2__less_0) ).

thf(2621,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) @ ( c_Finite__Set_Ocard @ A @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ D ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(719,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/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

thf(2790,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)],[719]) ).

thf(663,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/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__commute_0) ).

thf(2660,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)],[663]) ).

thf(287,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).

thf(1768,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(328,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( c_Finite__Set_Ofold @ C @ D @ B @ E @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ E )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ C @ D @ J @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__fold__sup_0) ).

thf(1868,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( c_Finite__Set_Ofold @ C @ D @ B @ E @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ E )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ C @ D @ J @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(408,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/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).

thf(2061,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)],[408]) ).

thf(1052,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/sandbox2/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).

thf(3550,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)],[1052]) ).

thf(383,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).

thf(2000,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(271,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/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).

thf(1730,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)],[271]) ).

thf(830,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/sandbox2/benchmark/theBenchmark.p',cls_fold1__Un_0) ).

thf(3037,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)],[830]) ).

thf(35,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).

thf(1163,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)],[35]) ).

thf(57,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/sandbox2/benchmark/theBenchmark.p',cls_add__sup__distrib__left_0) ).

thf(1223,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)],[57]) ).

thf(488,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

thf(2249,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(613,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
       != ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
      | ( C = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).

thf(2541,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
       != ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
      | ( C = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(178,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).

thf(1519,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(69,axiom,
    class_Orderings_Oorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(1255,plain,
    class_Orderings_Oorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ C )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

thf(1123,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(200,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ E @ A @ C @ D ) @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__le__mapE_0) ).

thf(1570,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ E @ A @ C @ D ) @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(55,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/sandbox2/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).

thf(1217,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)],[55]) ).

thf(280,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 ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).

thf(1751,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 ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) ) @ 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)],[280]) ).

thf(845,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__valids @ A @ B @ C )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__sound_0) ).

thf(3069,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__valids @ A @ B @ C )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(973,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/sandbox2/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

thf(3371,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)],[973]) ).

thf(873,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_2) ).

thf(3134,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(311,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/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).

thf(1824,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)],[311]) ).

thf(396,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/sandbox2/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).

thf(2032,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)],[396]) ).

thf(438,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).

thf(2132,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(1036,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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

thf(3514,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)],[1036]) ).

thf(389,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

thf(2015,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)],[389]) ).

thf(78,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(1274,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)],[78]) ).

thf(668,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/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

thf(2673,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)],[668]) ).

thf(684,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_in @ A ) @ C ) @ D ) )
      | ~ ( 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/sandbox2/benchmark/theBenchmark.p',cls_below__fold1__iff_0) ).

thf(2705,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_in @ A ) @ C ) @ D ) )
      | ~ ( 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)],[684]) ).

thf(494,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 @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__ge_0) ).

thf(2264,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 @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(340,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(1900,plain,
    class_Orderings_Olinorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(268,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Map_Omap__le @ B @ A @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__antisym_0) ).

thf(1723,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_Map_Omap__le @ B @ A @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(637,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).

thf(2601,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(563,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Map_Odom @ A @ D @ E ) ) )
      | ~ ( c_Map_Omap__le @ A @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__def_0) ).

thf(2428,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Map_Odom @ A @ D @ E ) ) )
      | ~ ( c_Map_Omap__le @ A @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(695,axiom,
    ! [A: $i] :
      ( ( c_Hoare__Mirabelle_OMGT @ A )
      = ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ A @ ( c_Natural_Oevalc @ A ) @ tc_Com_Ostate ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGT__def_0) ).

thf(2733,plain,
    ! [A: $i] :
      ( ( c_Hoare__Mirabelle_OMGT @ A )
      = ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ A @ ( c_Natural_Oevalc @ A ) @ tc_Com_Ostate ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(726,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

thf(2805,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(499,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

thf(2277,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(111,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/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

thf(1355,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)],[111]) ).

thf(205,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).

thf(1580,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ 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)],[205]) ).

thf(1016,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ tc_Com_Ostate ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) ) @ tc_Com_Ostate )
      | ~ ( c_Hoare__Mirabelle_Ohoare__valids @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ tc_Com_Ostate ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) ) @ tc_Com_Ostate )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Hoare__Mirabelle_OMGT @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) ) @ tc_Com_Ostate ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGF__complete_0) ).

thf(3471,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ tc_Com_Ostate ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) ) @ tc_Com_Ostate )
      | ~ ( c_Hoare__Mirabelle_Ohoare__valids @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ tc_Com_Ostate ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) ) @ tc_Com_Ostate )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Hoare__Mirabelle_OMGT @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) ) @ tc_Com_Ostate ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(334,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

thf(1883,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(214,axiom,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

thf(1602,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(565,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/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(2433,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)],[565]) ).

thf(363,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

thf(1951,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).

thf(1888,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(468,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).

thf(2200,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)],[468]) ).

thf(459,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

thf(2179,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)],[459]) ).

thf(33,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/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(1159,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)],[33]) ).

thf(528,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/sandbox2/benchmark/theBenchmark.p',cls_Max__mono_0) ).

thf(2345,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)],[528]) ).

thf(132,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

thf(1407,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)],[132]) ).

thf(480,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ E ) @ ( tc_fun @ D @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ E @ ( tc_fun @ D @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__minus_0) ).

thf(2228,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ E ) @ ( tc_fun @ D @ tc_bool ) )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ E @ ( tc_fun @ D @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(1093,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 ) ) )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

thf(3647,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 ) ) )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).

thf(6,axiom,
    class_Ring__and__Field_Ocomm__semiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

thf(1106,plain,
    class_Ring__and__Field_Ocomm__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).

thf(1423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(947,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

thf(3307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).

thf(930,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Orestrict__map @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ C @ D )
      = ( c_Map_Orestrict__map @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ E ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__restrict_0) ).

thf(3271,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Orestrict__map @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ C @ D )
      = ( c_Map_Orestrict__map @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ E ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

thf(571,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Map_Orestrict__map @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a @ B ) @ v_x )
      = ( c_Option_Ooption_ONone @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__map__to__empty_0) ).

thf(2445,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Map_Orestrict__map @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a @ B ) @ v_x )
      = ( c_Option_Ooption_ONone @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(896,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

thf(3191,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).

thf(579,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
       != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
      | ( C = D )
      | ( C = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(2464,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
       != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
      | ( C = D )
      | ( C = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(755,axiom,
    c_Finite__Set_Ofinite @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) @ tc_Com_Opname,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__dom__body_0) ).

thf(2873,plain,
    c_Finite__Set_Ofinite @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) @ tc_Com_Opname,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(115,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).

thf(1365,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(648,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ D ) @ B @ ( tc_Option_Ooption @ A ) ) @ B @ A )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__eq__singleton__conv_1) ).

thf(2628,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ D ) @ B @ ( tc_Option_Ooption @ A ) ) @ B @ A )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(667,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
        = ( c_Finite__Set_Ofold @ A @ C @ D @ B @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ D ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ B )
      | ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__eq__fold_0) ).

thf(2670,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
        = ( c_Finite__Set_Ofold @ A @ C @ D @ B @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ D ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ B )
      | ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(988,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(3403,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).

thf(622,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
       != ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
      | ( A = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).

thf(2565,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
       != ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
      | ( A = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(664,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ A @ C @ D )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv2_1) ).

thf(2663,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ A @ C @ D )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(194,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ A @ B @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__refl_0) ).

thf(1555,plain,
    ! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ A @ A @ B @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(732,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/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).

thf(2820,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)],[732]) ).

thf(1029,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).

thf(3499,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).

thf(843,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).

thf(3065,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)],[843]) ).

thf(1055,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ofold @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ C )
        = ( hAPP @ ( hAPP @ A @ D ) @ ( c_Finite__Set_Ofold @ A @ B @ E @ C @ C ) ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C )
      | ~ ( c_Lattices_Olower__semilattice @ F @ G @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ofold__inf__insert_0) ).

thf(3556,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ofold @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ C )
        = ( hAPP @ ( hAPP @ A @ D ) @ ( c_Finite__Set_Ofold @ A @ B @ E @ C @ C ) ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C )
      | ~ ( c_Lattices_Olower__semilattice @ F @ G @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).

thf(1073,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).

thf(3600,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)],[1073]) ).

thf(253,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( hAPP @ D @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ A @ D @ E @ C ) @ B )
        = ( c_Option_Ooption_ONone @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_2) ).

thf(1687,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( hAPP @ D @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ A @ D @ E @ C ) @ B )
        = ( c_Option_Ooption_ONone @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(152,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).

thf(1457,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(615,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/sandbox2/benchmark/theBenchmark.p',cls_card__psubset_0) ).

thf(2547,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)],[615]) ).

thf(514,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/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(2313,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)],[514]) ).

thf(828,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__greatest_0) ).

thf(3033,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)],[828]) ).

thf(990,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ C )
      = ( c_The @ ( c_Finite__Set_Ofold1Set @ A @ C @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__def_0) ).

thf(3408,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ C )
      = ( c_The @ ( c_Finite__Set_Ofold1Set @ A @ C @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(1071,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/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

thf(3595,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)],[1071]) ).

thf(710,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

thf(2769,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)],[710]) ).

thf(1005,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

thf(3445,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).

thf(861,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ C @ D @ A @ B @ E ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).

thf(3105,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ C @ D @ A @ B @ E ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(541,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

thf(2377,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(364,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

thf(1953,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(765,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).

thf(2895,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(626,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(2577,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(11,axiom,
    class_Ring__and__Field_Oordered__semiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).

thf(1111,plain,
    class_Ring__and__Field_Oordered__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(139,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/sandbox2/benchmark/theBenchmark.p',cls_less__supI2_0) ).

thf(1425,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)],[139]) ).

thf(1094,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).

thf(3650,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)],[1094]) ).

thf(916,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).

thf(3237,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(812,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/sandbox2/benchmark/theBenchmark.p',cls_fold1__Un2_0) ).

thf(3001,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)],[812]) ).

thf(820,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/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(3018,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)],[820]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

thf(1360,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(486,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(2245,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)],[486]) ).

thf(593,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(2498,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(187,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).

thf(1541,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( 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)],[187]) ).

thf(923,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Orestrict__map @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ F @ D @ E )
        = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ F @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__fun__upd_0) ).

thf(3254,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Orestrict__map @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ F @ D @ E )
        = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ F @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).

thf(992,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).

thf(3413,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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)],[992]) ).

thf(321,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).

thf(1851,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(289,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ E @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ E @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__trans_0) ).

thf(1772,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ E @ B @ C @ D )
      | ~ ( c_Map_Omap__le @ A @ E @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(71,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/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).

thf(1259,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)],[71]) ).

thf(868,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oless__infI2_0) ).

thf(3122,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)],[868]) ).

thf(742,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

thf(2841,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)],[742]) ).

thf(101,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/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).

thf(1328,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)],[101]) ).

thf(800,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(2973,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(16,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).

thf(1121,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ 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)],[16]) ).

thf(170,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).

thf(1498,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)],[170]) ).

thf(208,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).

thf(1587,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(598,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__inf__iff_0) ).

thf(2509,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)],[598]) ).

thf(860,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Map_Odom @ A @ D @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domIff_0) ).

thf(3102,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Map_Odom @ A @ D @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(247,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).

thf(1672,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(332,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/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(1878,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)],[332]) ).

thf(980,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/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(3386,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)],[980]) ).

thf(23,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(1138,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(692,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ B @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ ( c_Map_Odom @ A @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I2_J_0) ).

thf(2724,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ B @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ ( c_Map_Odom @ A @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(266,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

thf(1719,plain,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(749,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/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).

thf(2858,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)],[749]) ).

thf(496,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
        = C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ C @ I @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).

thf(2268,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
        = C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ C @ I @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(1003,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).

thf(3440,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( 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)],[1003]) ).

thf(199,axiom,
    ! [A: $i] :
      ( A
     != ( c_Suc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

thf(1567,plain,
    ! [A: $i] :
      ( A
     != ( c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(955,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( ( c_Finite__Set_Ofold__image @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ F ) @ A @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ B @ E ) ) @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ C @ F @ A @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ F ) )
      | ~ ( c_Finite__Set_Ofinite @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__image__insert_0) ).

thf(3326,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( ( c_Finite__Set_Ofold__image @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ F ) @ A @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ B @ E ) ) @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ C @ F @ A @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ F ) )
      | ~ ( c_Finite__Set_Ofinite @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).

thf(359,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) ) @ C ) ) @ D ) ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).

thf(1942,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) ) @ C ) ) @ D ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(1083,axiom,
    class_Orderings_Oorder @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(3622,plain,
    class_Orderings_Oorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).

thf(405,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).

thf(2053,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(998,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_1) ).

thf(3428,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)],[998]) ).

thf(657,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

thf(2649,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)],[657]) ).

thf(716,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).

thf(2781,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(577,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/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(2460,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)],[577]) ).

thf(168,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_Finite__Set_Ofun__left__comm @ ( c_HOL_Oplus__class_Oplus @ A ) @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofun__left__comm_0) ).

thf(1493,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_Finite__Set_Ofun__left__comm @ ( c_HOL_Oplus__class_Oplus @ A ) @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(723,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ D @ C )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__fun__upd_0) ).

thf(2798,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ D @ C )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ A @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(737,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

thf(2830,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(42,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

thf(1182,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(816,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
        = ( c_Suc @ ( c_Finite__Set_Ocard @ C @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert__if_1) ).

thf(3010,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
        = ( c_Suc @ ( c_Finite__Set_Ocard @ C @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(575,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B )
       != ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).

thf(2455,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B )
       != ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(642,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ D ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit_1) ).

thf(2613,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ D ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(357,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Finite__Set_Ofun__left__comm @ A @ B @ B )
      | ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofun__left__comm_0) ).

thf(1937,plain,
    ! [B: $i,A: $i] :
      ( ( c_Finite__Set_Ofun__left__comm @ A @ B @ B )
      | ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(429,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ B @ A )
        = ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__fold__sup_0) ).

thf(2108,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ B @ A )
        = ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(148,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) )
        = ( c_Finite__Set_Ofold @ A @ B @ D @ E @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ E )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ C @ F @ G @ H @ A @ I @ J @ K @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_Oinf__Inf__fold__inf_0) ).

thf(1446,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) )
        = ( c_Finite__Set_Ofold @ A @ B @ D @ E @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ E )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ C @ F @ G @ H @ A @ I @ J @ K @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(617,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/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).

thf(2551,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)],[617]) ).

thf(51,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/sandbox2/benchmark/theBenchmark.p',cls_less__infI1_0) ).

thf(1207,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)],[51]) ).

thf(517,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ D @ A ) @ ( hAPP @ B @ E ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1_0) ).

thf(2317,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ D @ A ) @ ( hAPP @ B @ E ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(940,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/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).

thf(3294,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)],[940]) ).

thf(918,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ E @ A ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ E @ tc_bool ) ) @ D ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff_0) ).

thf(3242,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ E @ A ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ E @ tc_bool ) ) @ D ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).

thf(99,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(1324,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)],[99]) ).

thf(1047,axiom,
    class_Finite__Set_Ofinite_Ofinite @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).

thf(3540,plain,
    class_Finite__Set_Ofinite_Ofinite @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).

thf(377,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).

thf(1984,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)],[377]) ).

thf(729,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Complete__Lattice_Ocomplete__lattice @ A @ B @ ( c_COMBC @ C @ D @ D @ tc_bool ) @ ( c_COMBC @ E @ D @ D @ tc_bool ) @ F @ G @ H @ I @ D )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ A @ C @ E @ G @ F @ I @ H @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).

thf(2813,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Complete__Lattice_Ocomplete__lattice @ A @ B @ ( c_COMBC @ C @ D @ D @ tc_bool ) @ ( c_COMBC @ E @ D @ D @ tc_bool ) @ F @ G @ H @ I @ D )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ A @ C @ E @ G @ F @ I @ H @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(267,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

thf(1720,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)],[267]) ).

thf(907,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) @ ( c_Finite__Set_Ocard @ A @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Diff1__less_0) ).

thf(3215,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) @ ( c_Finite__Set_Ocard @ A @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(291,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/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

thf(1776,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)],[291]) ).

thf(73,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

thf(1263,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(1096,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ A ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ D @ C @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv2_0) ).

thf(3656,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ A ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ D @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).

thf(573,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(2450,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(1023,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__iff_2) ).

thf(3486,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).

thf(1,negated_conjecture,
    ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ v_x ) @ v_x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(1099,plain,
    ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ v_x ) @ v_x ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(67,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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(1249,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)],[67]) ).

thf(603,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/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_0) ).

thf(2519,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)],[603]) ).

thf(870,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
        = ( c_Finite__Set_Ofold @ ( c_Set_Oinsert @ A ) @ C @ B @ A @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_union__fold__insert_0) ).

thf(3126,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
        = ( c_Finite__Set_Ofold @ ( c_Set_Oinsert @ A ) @ C @ B @ A @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(1048,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

thf(3541,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).

thf(183,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Option_Ooption_Ooption__case @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ C )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I4_J_0) ).

thf(1530,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Option_Ooption_Ooption__case @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ C )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(122,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).

thf(1382,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(588,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Un_0) ).

thf(2487,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(744,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(2845,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(840,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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(3059,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)],[840]) ).

thf(192,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).

thf(1552,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)],[192]) ).

thf(746,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/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

thf(2851,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)],[746]) ).

thf(532,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 @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__lower_0) ).

thf(2355,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 @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(355,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).

thf(1932,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)],[355]) ).

thf(596,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(2505,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)],[596]) ).

thf(982,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).

thf(3390,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)],[982]) ).

thf(1086,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ B ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(3628,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).

thf(865,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
        = C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).

thf(3115,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
        = C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(141,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).

thf(1429,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(920,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__trans_0) ).

thf(3247,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)],[920]) ).

thf(751,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/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

thf(2862,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)],[751]) ).

thf(213,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).

thf(1599,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(680,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).

thf(2697,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(863,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ A @ tc_bool ) ) )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).

thf(3109,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ A @ tc_bool ) ) )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(375,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/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).

thf(1979,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)],[375]) ).

thf(884,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).

thf(3162,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(284,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

thf(1759,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Suc @ A )
       != ( c_Suc @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(127,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).

thf(1393,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(1018,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(3476,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(96,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/sandbox2/benchmark/theBenchmark.p',cls_le__maxI2_0) ).

thf(1318,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)],[96]) ).

thf(469,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).

thf(2203,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(292,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/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).

thf(1779,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)],[292]) ).

thf(471,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).

thf(2208,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(934,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 @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ D ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ C )
      | ~ ( c_Lattices_Olower__semilattice @ A @ F @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ofold1__belowI_0) ).

thf(3279,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 @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ D ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ C )
      | ~ ( c_Lattices_Olower__semilattice @ A @ F @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).

thf(256,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).

thf(1695,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)],[256]) ).

thf(156,axiom,
    class_Lattices_Odistrib__lattice @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).

thf(1466,plain,
    class_Lattices_Odistrib__lattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(568,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(2440,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)],[568]) ).

thf(477,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/sandbox2/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).

thf(2221,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)],[477]) ).

thf(1033,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

thf(3508,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)],[1033]) ).

thf(221,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_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).

thf(1616,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_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( 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)],[221]) ).

thf(608,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).

thf(2529,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ D @ C @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(272,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_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ A @ B )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A @ B ) ) @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__Un__disjoint_0) ).

thf(1732,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_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ A @ B )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A @ B ) ) @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(878,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
        = ( hAPP @ A @ F ) )
      | ( F = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).

thf(3147,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)],[878]) ).

thf(1009,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ F ) @ A @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ E ) ) @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ F @ A @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ F ) )
      | ~ ( c_Finite__Set_Ofinite @ F @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__image__insert_0) ).

thf(3454,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ F ) @ A @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ E ) ) @ ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ F @ A @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ F ) )
      | ~ ( c_Finite__Set_Ofinite @ F @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).

thf(651,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 @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__strict__below__iff_2) ).

thf(2634,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 @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
      | ( 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)],[651]) ).

thf(143,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).

thf(1434,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(64,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).

thf(1241,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)],[64]) ).

thf(706,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).

thf(2761,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(319,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oab__semigroup__idem__mult__inf_0) ).

thf(1846,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)],[319]) ).

thf(263,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).

thf(1712,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(946,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(3306,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)],[946]) ).

thf(415,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/sandbox2/benchmark/theBenchmark.p',cls_add__sup__distrib__right_0) ).

thf(2076,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)],[415]) ).

thf(701,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__binary_0) ).

thf(2748,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(38,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).

thf(1170,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)],[38]) ).

thf(795,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ C ) @ D ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).

thf(2963,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ C ) @ D ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(953,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != ( c_Com_Ocom_OBODY @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).

thf(3321,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != ( c_Com_Ocom_OBODY @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).

thf(554,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/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

thf(2408,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)],[554]) ).

thf(243,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).

thf(1663,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(434,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).

thf(2121,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(343,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B @ C @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__inf__le__inf_0) ).

thf(1906,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B @ C @ A @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(783,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__subset__iff_0) ).

thf(2936,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(556,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubsetD_0) ).

thf(2413,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

thf(1754,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(3,axiom,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).

thf(1103,plain,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(924,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Com_Ocom_OBODY @ D ) @ E @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Com_Ocom_OBODY @ D ) @ E @ B ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ D ) @ tc_Com_Ocom ) @ E @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BodyN_0) ).

thf(3257,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Com_Ocom_OBODY @ D ) @ E @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Com_Ocom_OBODY @ D ) @ E @ B ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ D ) @ tc_Com_Ocom ) @ E @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).

thf(164,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

thf(1483,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)],[164]) ).

thf(278,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).

thf(1747,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(926,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ A @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_1) ).

thf(3262,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)],[926]) ).

thf(1040,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__singleton_0) ).

thf(3523,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).

thf(119,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).

thf(1374,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)],[119]) ).

thf(670,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(2677,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(457,axiom,
    ! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__empty_0) ).

thf(2176,plain,
    ! [C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(606,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(2524,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(985,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ A @ B ) @ B )
        = B )
      | ~ ( c_OrderedGroup_Oab__semigroup__idem__mult @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Omult__idem_0) ).

thf(3396,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)],[985]) ).

thf(30,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 @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__belowI_0) ).

thf(1154,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 @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(894,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/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(3187,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)],[894]) ).

thf(693,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).

thf(2727,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(1031,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).

thf(3504,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).

thf(1038,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( c_Finite__Set_Osetprod @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ B @ D ) ) @ ( c_Finite__Set_Osetprod @ B @ E @ C @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__insert_0) ).

thf(3519,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( c_Finite__Set_Osetprod @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ B @ D ) ) @ ( c_Finite__Set_Osetprod @ B @ E @ C @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).

thf(1077,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/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

thf(3609,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)],[1077]) ).

thf(463,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/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).

thf(2188,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)],[463]) ).

thf(125,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_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).

thf(1388,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_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ 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)],[125]) ).

thf(185,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

thf(1535,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)],[185]) ).

thf(550,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ D @ E )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Map_Odom @ A @ D @ E ) ) )
      | ( C
        = ( c_Option_Ooption_ONone @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__fun__upd_1) ).

thf(2398,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ D @ E )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Map_Odom @ A @ D @ E ) ) )
      | ( C
        = ( c_Option_Ooption_ONone @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(1075,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/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

thf(3604,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)],[1075]) ).

thf(369,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).

thf(1965,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)],[369]) ).

thf(731,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B ) ) @ B ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__in_0) ).

thf(2817,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ B ) ) @ B ) )
      | ( 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)],[731]) ).

thf(439,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/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(2134,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)],[439]) ).

thf(798,axiom,
    class_Lattices_Olower__semilattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

thf(2970,plain,
    class_Lattices_Olower__semilattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(952,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_4) ).

thf(3319,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)],[952]) ).

thf(1089,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__iff_1) ).

thf(3636,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).

thf(915,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ A @ B @ C @ D ) )
       != ( hAPP @ B @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ A @ B @ C @ D ) ) )
      | ( c_Map_Omap__le @ A @ B @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__def_2) ).

thf(3234,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ A @ B @ C @ D ) )
       != ( hAPP @ B @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ A @ B @ C @ D ) ) )
      | ( c_Map_Omap__le @ A @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(784,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D )
      = ( c_HOL_Ominus__class_Ominus @ ( 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 ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

thf(2938,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D )
      = ( c_HOL_Ominus__class_Ominus @ ( 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 ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(720,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/sandbox2/benchmark/theBenchmark.p',cls_Min__Un_0) ).

thf(2791,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)],[720]) ).

thf(917,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 ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

thf(3240,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 ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).

thf(223,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

thf(1620,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)],[223]) ).

thf(589,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq2_0) ).

thf(2489,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(548,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/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

thf(2393,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)],[548]) ).

thf(853,axiom,
    ! [A: $i] :
      ( ( c_Option_Oset @ ( c_Option_Ooption_ONone @ A ) @ A )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty__eq_1) ).

thf(3086,plain,
    ! [A: $i] :
      ( ( c_Option_Oset @ ( c_Option_Ooption_ONone @ A ) @ A )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(239,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ B @ E )
        = ( c_Option_Ooption_ONone @ D ) )
      | ( ( hAPP @ B @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__SomeD_0) ).

thf(1652,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ B @ E )
        = ( c_Option_Ooption_ONone @ D ) )
      | ( ( hAPP @ B @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(353,axiom,
    class_Lattices_Olattice @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

thf(1929,plain,
    class_Lattices_Olattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(58,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
        = ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__diff__distrib__left_0) ).

thf(1226,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
        = ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(679,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/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).

thf(2695,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)],[679]) ).

thf(70,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__triv_0) ).

thf(1256,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(793,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(2959,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)],[793]) ).

thf(906,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ A @ B ) ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ E ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ A ) @ C ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).

thf(3213,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ A @ B ) ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ E ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ A ) @ C ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(866,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
      | ~ ( c_Orderings_Olinorder @ D @ C @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv3_0) ).

thf(3118,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
      | ~ ( c_Orderings_Olinorder @ D @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(506,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

thf(2293,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(231,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/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(1635,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)],[231]) ).

thf(7,axiom,
    class_Ring__and__Field_Omult__mono @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).

thf(1107,plain,
    class_Ring__and__Field_Omult__mono @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(103,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

thf(1332,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)],[103]) ).

thf(406,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/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(2055,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)],[406]) ).

thf(945,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/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

thf(3304,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)],[945]) ).

thf(445,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( B = E )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ E @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ F ) @ G @ ( tc_Option_Ooption @ C ) ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_4) ).

thf(2148,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( B = E )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ E @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ F ) @ G @ ( tc_Option_Ooption @ C ) ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(1043,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ D ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit__asm_1) ).

thf(3532,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ t_b ) @ D ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ ( hAPP @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).

thf(911,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/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

thf(3223,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)],[911]) ).

thf(450,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) @ A @ A )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B @ D @ A @ A ) ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__sup__insert_0) ).

thf(2161,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) @ A @ A )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B @ D @ A @ A ) ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(24,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).

thf(1139,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)],[24]) ).

thf(172,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/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).

thf(1503,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)],[172]) ).

thf(465,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).

thf(2193,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(823,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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(3023,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)],[823]) ).

thf(395,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

thf(2029,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(520,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Osetsum @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ tc_nat )
        = ( c_Finite__Set_Osetsum @ A @ B @ C @ tc_nat ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1__nat_1) ).

thf(2326,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Osetsum @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ tc_nat )
        = ( c_Finite__Set_Osetsum @ A @ B @ C @ tc_nat ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(763,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).

thf(2891,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(77,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).

thf(1271,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)],[77]) ).

thf(512,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/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(2308,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)],[512]) ).

thf(118,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).

thf(1371,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)],[118]) ).

thf(849,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/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Ofold1__Un2_0) ).

thf(3077,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)],[849]) ).

thf(904,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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).

thf(3208,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)],[904]) ).

thf(327,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/sandbox2/benchmark/theBenchmark.p',cls_Max__def__raw_0) ).

thf(1865,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)],[327]) ).

thf(960,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ D @ A @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__leE_0) ).

thf(3340,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ D @ A @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).

thf(63,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).

thf(1239,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(382,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).

thf(1997,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(1082,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/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(3619,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)],[1082]) ).

thf(1064,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/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__Un_0) ).

thf(3579,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)],[1064]) ).

thf(339,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/sandbox2/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).

thf(1897,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)],[339]) ).

thf(619,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_conseq_0) ).

thf(2557,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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)],[619]) ).

thf(1091,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ofold @ A @ B @ C @ D @ E )
        = ( hAPP @ ( hAPP @ A @ F ) @ ( c_Finite__Set_Ofold @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ F ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ D )
      | ~ ( c_Finite__Set_Ofun__left__comm @ A @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_Ofold__rec_0) ).

thf(3641,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ofold @ A @ B @ C @ D @ E )
        = ( hAPP @ ( hAPP @ A @ F ) @ ( c_Finite__Set_Ofold @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ F ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ D )
      | ~ ( c_Finite__Set_Ofun__left__comm @ A @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).

thf(855,axiom,
    class_HOL_Ominus @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).

thf(3091,plain,
    class_HOL_Ominus @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(155,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 ) @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) ) @ C ) ) @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).

thf(1464,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 ) @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) ) @ C ) ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(233,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).

thf(1638,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(966,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( c_Option_Ooption_ONone @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit_0) ).

thf(3355,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( c_Option_Ooption_Ooption__case @ B @ C @ ( c_Option_Ooption_ONone @ t_b ) @ t_a @ t_b ) ) )
      | ( hBOOL @ ( hAPP @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

thf(1194,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(416,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).

thf(2079,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)],[416]) ).

thf(604,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).

thf(2521,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(671,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).

thf(2679,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)],[671]) ).

thf(202,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

thf(1574,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(770,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__Int_0) ).

thf(2906,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)],[770]) ).

thf(26,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).

thf(1144,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)],[26]) ).

thf(899,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_in @ A ) @ D ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).

thf(3197,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_in @ A ) @ D ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).

thf(979,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_0) ).

thf(3384,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)],[979]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).

thf(1439,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(410,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).

thf(2065,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( 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)],[410]) ).

thf(52,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).

thf(1209,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)],[52]) ).

thf(690,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).

thf(2721,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(612,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/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__left__commute_0) ).

thf(2538,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)],[612]) ).

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 ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ D ) @ B ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).

thf(1853,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)],[322]) ).

thf(81,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).

thf(1282,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(584,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff_0) ).

thf(2478,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
      | ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(922,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ofold @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ F )
        = ( hAPP @ ( hAPP @ A @ D ) @ ( c_Finite__Set_Ofold @ A @ B @ E @ C @ F ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C )
      | ~ ( c_Finite__Set_Ofun__left__comm @ A @ C @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_Ofold__insert_0) ).

thf(3251,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ofold @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ F )
        = ( hAPP @ ( hAPP @ A @ D ) @ ( c_Finite__Set_Ofold @ A @ B @ E @ C @ F ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C )
      | ~ ( c_Finite__Set_Ofun__left__comm @ A @ C @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).

thf(446,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/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(2151,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)],[446]) ).

thf(881,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

thf(3155,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)],[881]) ).

thf(418,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 ) @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) ) @ C ) ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).

thf(2084,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 ) @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) ) @ 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)],[418]) ).

thf(474,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/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).

thf(2214,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)],[474]) ).

thf(557,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ D @ C @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__less__iff__gr__or__eq_0) ).

thf(2415,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ D @ C @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(338,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).

thf(1894,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)],[338]) ).

thf(806,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/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

thf(2987,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)],[806]) ).

thf(652,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/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

thf(2637,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)],[652]) ).

thf(560,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

thf(2422,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(712,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(2774,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)],[712]) ).

thf(937,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olattice__class_OInf__fin @ A ) @ B )
        = ( c_Complete__Lattice_OInf__class_OInf @ B @ A ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__fin__Inf_0) ).

thf(3287,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olattice__class_OInf__fin @ A ) @ B )
        = ( c_Complete__Lattice_OInf__class_OInf @ 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)],[937]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).

thf(1524,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(109,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/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

thf(1349,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)],[109]) ).

thf(929,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

thf(3270,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).

thf(209,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_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).

thf(1589,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_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(502,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ D ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ A @ G @ H @ I @ J @ K @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).

thf(2284,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ D ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ A @ G @ H @ I @ J @ K @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(215,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).

thf(1603,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)],[215]) ).

thf(509,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B ) ) @ B ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__in_0) ).

thf(2299,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B ) ) @ B ) )
      | ( 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)],[509]) ).

thf(432,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).

thf(2116,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)],[432]) ).

thf(741,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ C @ D @ E ) @ ( hAPP @ ( hAPP @ A @ F ) @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ F ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ G ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).

thf(2839,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ C @ D @ E ) @ ( hAPP @ ( hAPP @ A @ F ) @ G ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ F ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(786,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/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

thf(2943,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)],[786]) ).

thf(787,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofold @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__empty_0) ).

thf(2945,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofold @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(1067,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/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(3586,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)],[1067]) ).

thf(254,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( D = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_2) ).

thf(1690,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( D = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(892,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Odom @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ( A
        = ( c_COMBK @ ( c_Option_Ooption_ONone @ C ) @ ( tc_Option_Ooption @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__eq__empty__conv_0) ).

thf(3182,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Odom @ A @ B @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
      | ( A
        = ( c_COMBK @ ( c_Option_Ooption_ONone @ C ) @ ( tc_Option_Ooption @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(467,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/sandbox2/benchmark/theBenchmark.p',cls_add__eq__inf__sup_0) ).

thf(2197,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)],[467]) ).

thf(371,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ C @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

thf(1969,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ C @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(245,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

thf(1667,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(460,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/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(2182,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)],[460]) ).

thf(159,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).

thf(1471,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(650,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/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(2632,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)],[650]) ).

thf(228,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/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

thf(1630,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)],[228]) ).

thf(1061,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/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

thf(3572,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)],[1061]) ).

thf(704,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ ( c_Option_Ooption_ONone @ D ) @ C @ ( tc_Option_Ooption @ D ) )
        = ( c_Map_Orestrict__map @ A @ B @ C @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__None__restrict_1) ).

thf(2757,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ ( c_Option_Ooption_ONone @ D ) @ C @ ( tc_Option_Ooption @ D ) )
        = ( c_Map_Orestrict__map @ A @ B @ C @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(885,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

thf(3165,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(195,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).

thf(1556,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(489,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(2252,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(85,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).

thf(1293,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(780,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__iff__inf_0) ).

thf(2928,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)],[780]) ).

thf(12,axiom,
    class_Ring__and__Field_Omult__zero @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

thf(1112,plain,
    class_Ring__and__Field_Omult__zero @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(909,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/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(3219,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)],[909]) ).

thf(734,axiom,
    class_Orderings_Opreorder @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(2824,plain,
    class_Orderings_Opreorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(639,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( C = B )
      | ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ D @ A @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oless__linear_0) ).

thf(2605,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( C = B )
      | ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ D @ A @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(825,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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(3027,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)],[825]) ).

thf(515,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Option_Oset @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_elem__set_1) ).

thf(2314,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Option_Oset @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(437,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).

thf(2129,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)],[437]) ).

thf(527,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(2343,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(647,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/sandbox2/benchmark/theBenchmark.p',cls_Max__Un_0) ).

thf(2625,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)],[647]) ).

thf(430,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).

thf(2111,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(847,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageI_0) ).

thf(3073,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Set_Ovimage @ C @ D @ A @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ ( hAPP @ C @ B ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(493,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
        = ( hAPP @ ( hAPP @ E @ C ) @ D ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).

thf(2261,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
        = ( hAPP @ ( hAPP @ E @ C ) @ D ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(310,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/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

thf(1821,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)],[310]) ).

thf(778,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/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

thf(2923,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)],[778]) ).

thf(316,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) ) @ C ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).

thf(1838,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) ) @ C ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(1079,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofold__image @ A @ B @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__image__empty_0) ).

thf(3614,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofold__image @ A @ B @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).

thf(814,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).

thf(3006,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)],[814]) ).

thf(1008,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/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(3451,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)],[1008]) ).

thf(28,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(1149,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)],[28]) ).

thf(942,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/sandbox2/benchmark/theBenchmark.p',cls_empty_0) ).

thf(3298,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)],[942]) ).

thf(756,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/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

thf(2874,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)],[756]) ).

thf(1021,axiom,
    class_Lattices_Oupper__semilattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(3483,plain,
    class_Lattices_Oupper__semilattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) )
        = ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B @ C @ A @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__Sup__fold__sup_0) ).

thf(1344,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) )
        = ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B @ C @ A @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(879,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_in @ A ) @ C ) @ D ) )
      | ~ ( 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/sandbox2/benchmark/theBenchmark.p',cls_strict__below__fold1__iff_0) ).

thf(3150,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_in @ A ) @ C ) @ D ) )
      | ~ ( 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)],[879]) ).

thf(521,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Olinorder @ ( c_COMBC @ A @ B @ B @ tc_bool ) @ ( c_COMBC @ C @ B @ B @ tc_bool ) @ B )
      | ~ ( c_Orderings_Olinorder @ A @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Odual__linorder_0) ).

thf(2329,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Olinorder @ ( c_COMBC @ A @ B @ B @ tc_bool ) @ ( c_COMBC @ C @ B @ B @ tc_bool ) @ B )
      | ~ ( c_Orderings_Olinorder @ A @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(686,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__empty_0) ).

thf(2710,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(309,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(1820,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(530,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

thf(2350,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(739,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_0) ).

thf(2835,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)],[739]) ).

thf(182,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

thf(1528,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)],[182]) ).

thf(235,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/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(1643,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)],[235]) ).

thf(442,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

thf(2139,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(40,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
     != ( c_COMBK @ ( c_Option_Ooption_ONone @ C ) @ ( tc_Option_Ooption @ C ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__nonempty_0) ).

thf(1176,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) )
     != ( c_COMBK @ ( c_Option_Ooption_ONone @ C ) @ ( tc_Option_Ooption @ C ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(13,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

thf(1113,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)],[13]) ).

thf(633,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/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).

thf(2592,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)],[633]) ).

thf(876,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ B ) )
      | ( C = B )
      | ~ ( c_Orderings_Olinorder @ D @ A @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_OneqE_0) ).

thf(3142,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ B ) )
      | ( C = B )
      | ~ ( c_Orderings_Olinorder @ D @ A @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(1035,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( c_Finite__Set_Ofold @ B @ C @ D @ E @ E ) ) @ ( hAPP @ ( hAPP @ B @ F ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ D ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ E )
      | ~ ( c_Lattices_Olower__semilattice @ A @ G @ B @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ofold__inf__le__inf_0) ).

thf(3512,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( c_Finite__Set_Ofold @ B @ C @ D @ E @ E ) ) @ ( hAPP @ ( hAPP @ B @ F ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ F ) @ D ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ E )
      | ~ ( c_Lattices_Olower__semilattice @ A @ G @ B @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).

thf(678,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

thf(2693,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(303,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/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).

thf(1805,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)],[303]) ).

thf(1046,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(3539,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).

thf(558,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/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).

thf(2418,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)],[558]) ).

thf(47,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).

thf(1198,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( 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)],[47]) ).

thf(317,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).

thf(1841,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(128,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ C @ D @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) @ F @ ( tc_Option_Ooption @ E ) ) @ D )
       != ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_1) ).

thf(1396,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ( ( hAPP @ ( c_Fun_Ofun__upd @ C @ D @ ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ A ) @ F @ ( tc_Option_Ooption @ E ) ) @ D )
       != ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OlessThan @ B @ A )
       != ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).

thf(1926,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OlessThan @ B @ A )
       != ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(536,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(2365,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(257,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).

thf(1699,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)],[257]) ).

thf(551,axiom,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Ominus @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).

thf(2401,plain,
    ! [B: $i,A: $i] :
      ( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
      | ~ ( class_HOL_Ominus @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(211,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

thf(1594,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)],[211]) ).

thf(473,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).

thf(2212,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)],[473]) ).

thf(455,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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

thf(2171,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)],[455]) ).

thf(404,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

thf(2051,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(996,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ A @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ ( c_Map_Odom @ B @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I3_J_0) ).

thf(3423,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ A @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ ( c_Map_Odom @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).

thf(883,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__Diff__lessThan_0) ).

thf(3159,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(538,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ D ) )
      | ~ ( 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/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__insert_0) ).

thf(2369,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ D ) )
      | ~ ( 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)],[538]) ).

thf(781,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ A )
        = ( c_Finite__Set_Osetsum @ B @ C @ D @ A ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1_1) ).

thf(2931,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ A )
        = ( c_Finite__Set_Osetsum @ B @ C @ D @ A ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(504,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).

thf(2288,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(392,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

thf(2022,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(948,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_OrderedGroup_Oab__semigroup__mult @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ononempty__iff_2) ).

thf(3310,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_OrderedGroup_Oab__semigroup__mult @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).

thf(611,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
        = ( c_Suc @ ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert_0) ).

thf(2535,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
        = ( c_Suc @ ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(425,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).

thf(2101,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ 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)],[425]) ).

thf(269,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/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).

thf(1726,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)],[269]) ).

thf(797,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E )
        = ( c_Option_Ooption_ONone @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__out_0) ).

thf(2967,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E )
        = ( c_Option_Ooption_ONone @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(547,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).

thf(2390,plain,
    ! [B: $i,A: $i] :
      ( ( c_Com_Ocom_OSemi @ A @ B )
     != c_Com_Ocom_OSKIP ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(811,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(2999,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(963,axiom,
    ! [A: $i] :
      ( ( c_Com_Ocom_OBODY @ A )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).

thf(3348,plain,
    ! [A: $i] :
      ( ( c_Com_Ocom_OBODY @ A )
     != c_Com_Ocom_OSKIP ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).

thf(448,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).

thf(2156,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(412,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/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).

thf(2069,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)],[412]) ).

thf(753,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E )
       != A )
      | ( ( hAPP @ A @ B )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).

thf(2867,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)],[753]) ).

thf(1025,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/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).

thf(3490,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)],[1025]) ).

thf(197,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

thf(1562,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)],[197]) ).

thf(362,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/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

thf(1948,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)],[362]) ).

thf(484,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ 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_Osetprod @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ E @ C @ B @ A ) ) @ ( c_Finite__Set_Osetprod @ E @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__Un__disjoint_0) ).

thf(2239,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ 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_Osetprod @ E @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ E @ C @ B @ A ) ) @ ( c_Finite__Set_Osetprod @ E @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(827,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/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_2) ).

thf(3031,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)],[827]) ).

thf(305,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

thf(1809,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)],[305]) ).

thf(422,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/sandbox2/benchmark/theBenchmark.p',cls_max__lattice_0) ).

thf(2096,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)],[422]) ).

thf(49,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).

thf(1203,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)],[49]) ).

thf(665,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq1_0) ).

thf(2665,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(137,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ E @ A @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__find__right_0) ).

thf(1420,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ E @ A @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(21,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/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).

thf(1134,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)],[21]) ).

thf(674,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(2684,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(491,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oless__infI1_0) ).

thf(2256,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)],[491]) ).

thf(939,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ D ) @ C ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).

thf(3292,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ D ) @ C ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(628,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Map_Odom @ B @ A @ C ) ) @ ( c_Map_Odom @ D @ A @ C ) ) )
      | ~ ( c_Map_Omap__le @ B @ D @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__implies__dom__le_0) ).

thf(2582,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Map_Odom @ B @ A @ C ) ) @ ( c_Map_Odom @ D @ A @ C ) ) )
      | ~ ( c_Map_Omap__le @ B @ D @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(226,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 ) @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) ) @ C ) ) @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).

thf(1626,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 ) @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) ) @ C ) ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(1039,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(3522,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).

thf(90,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).

thf(1304,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(330,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/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).

thf(1873,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)],[330]) ).

thf(897,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/sandbox2/benchmark/theBenchmark.p',cls_cut_0) ).

thf(3193,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)],[897]) ).

thf(36,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 ) ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C @ D @ A @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__le__fold__sup_0) ).

thf(1166,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 ) ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C @ D @ A @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(428,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

thf(2107,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(157,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).

thf(1467,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(809,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ofold @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ F )
        = ( c_Finite__Set_Ofold @ A @ ( hAPP @ ( hAPP @ A @ D ) @ B ) @ E @ C @ F ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C )
      | ~ ( c_Finite__Set_Ofun__left__comm @ A @ C @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_Ofold__insert2_0) ).

thf(2994,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ofold @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ F )
        = ( c_Finite__Set_Ofold @ A @ ( hAPP @ ( hAPP @ A @ D ) @ B ) @ E @ C @ F ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C )
      | ~ ( c_Finite__Set_Ofun__left__comm @ A @ C @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(717,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).

thf(2784,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(497,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/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

thf(2271,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)],[497]) ).

thf(903,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ A @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Olinear_0) ).

thf(3206,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ A @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

thf(595,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ A @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__le_1) ).

thf(2503,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ A @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(252,axiom,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

thf(1684,plain,
    ! [A: $i] :
      ( ( c_Suc @ A )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(79,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_Finite__Set_Ofold @ A @ C @ D @ E @ F ) )
        = ( c_Finite__Set_Ofold @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ E @ F ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ E )
      | ~ ( c_Finite__Set_Ofun__left__comm @ A @ E @ F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_Ofold__fun__comm_0) ).

thf(1277,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ A @ B ) @ ( c_Finite__Set_Ofold @ A @ C @ D @ E @ F ) )
        = ( c_Finite__Set_Ofold @ A @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D @ E @ F ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ E )
      | ~ ( c_Finite__Set_Ofun__left__comm @ A @ E @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(435,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

thf(2124,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)],[435]) ).

thf(635,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).

thf(2597,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(366,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

thf(1958,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(600,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ B )
        = ( c_Finite__Set_Ocard @ A @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Diff__singleton__if_1) ).

thf(2513,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ B )
        = ( c_Finite__Set_Ocard @ A @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(190,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

thf(1547,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(688,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__idem_0) ).

thf(2715,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)],[688]) ).

thf(367,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).

thf(1961,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(864,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/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(3112,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)],[864]) ).

thf(276,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).

thf(1743,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(851,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).

thf(3082,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(237,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 )
        = ( c_HOL_Ominus__class_Ominus @ ( 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 ) @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C )
      | ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__Un_0) ).

thf(1647,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 )
        = ( c_HOL_Ominus__class_Ominus @ ( 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 ) @ A ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ C )
      | ~ ( c_Finite__Set_Ofinite @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(1097,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ C @ D )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Map_Odom @ A @ C @ D ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__restrict_0) ).

thf(3659,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ C @ D )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Map_Odom @ A @ C @ D ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).

thf(68,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

thf(1252,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)],[68]) ).

thf(871,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/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(3129,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)],[871]) ).

thf(602,axiom,
    class_Lattices_Obounded__lattice @ tc_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

thf(2518,plain,
    class_Lattices_Obounded__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(913,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/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(3228,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)],[913]) ).

thf(300,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_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).

thf(1798,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_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(983,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/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).

thf(3391,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)],[983]) ).

thf(288,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
      | ( c_Finite__Set_Ofinite @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_0) ).

thf(1770,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)],[288]) ).

thf(975,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( 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 ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

thf(3376,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( 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 ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).

thf(177,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

thf(1516,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(950,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/sandbox2/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).

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 ) )
      | ~ ( 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)],[950]) ).

thf(802,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/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(2977,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)],[802]) ).

thf(219,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

thf(1611,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(540,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_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__subset__eq_0) ).

thf(2375,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_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ B ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ A ) @ A @ ( tc_fun @ A @ tc_bool ) @ tc_bool ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(31,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ 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 ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).

thf(1156,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ 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 ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(216,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).

thf(1605,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(631,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nitpick_Ofold__graph_H @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
      | ~ ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) ) @ ( tc_fun @ F @ tc_bool ) ) @ E @ F @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ F ) @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I2_J_0) ).

thf(2588,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Nitpick_Ofold__graph_H @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
      | ~ ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ F ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) ) @ ( tc_fun @ F @ tc_bool ) ) @ E @ F @ G )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ F ) @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(281,axiom,
    class_Lattices_Oupper__semilattice @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

thf(1753,plain,
    class_Lattices_Oupper__semilattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(545,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B )
      | ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).

thf(2386,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B )
      | ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(623,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/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(2569,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)],[623]) ).

thf(452,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).

thf(2165,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( 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)],[452]) ).

thf(842,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_2) ).

thf(3063,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)],[842]) ).

thf(43,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__class_OMin__def__raw_0) ).

thf(1186,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)],[43]) ).

thf(1054,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ B @ A )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__empty_0) ).

thf(3554,plain,
    ! [B: $i,A: $i] :
      ( ( c_Map_Odom @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ B @ A )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).

thf(901,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(3202,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(295,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

thf(1785,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(824,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(3026,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)],[824]) ).

thf(61,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_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).

thf(1235,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_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( 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)],[61]) ).

thf(285,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/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

thf(1763,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)],[285]) ).

thf(56,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).

thf(1220,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)],[56]) ).

thf(660,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(2656,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)],[660]) ).

thf(821,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ C @ A @ D )
      | ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv1_1) ).

thf(3019,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ C @ A @ D )
      | ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(850,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(3080,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)],[850]) ).

thf(297,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

thf(1790,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(265,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

thf(1716,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(478,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ C @ A @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oneq__iff_1) ).

thf(2224,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ C @ A @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(88,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/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(1300,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)],[88]) ).

thf(150,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
        = ( c_Finite__Set_Ofold @ A @ C @ D @ B @ B ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ B )
      | ~ ( c_OrderedGroup_Oab__semigroup__idem__mult @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Ofold1__eq__fold__idem_0) ).

thf(1452,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
        = ( c_Finite__Set_Ofold @ A @ C @ D @ B @ B ) )
      | ~ ( c_Finite__Set_Ofinite @ D @ B )
      | ~ ( c_OrderedGroup_Oab__semigroup__idem__mult @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(232,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

thf(1637,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(676,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ D ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).

thf(2688,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ D ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(931,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(3273,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(341,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

thf(1901,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)],[341]) ).

thf(1049,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/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(3544,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)],[1049]) ).

thf(241,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ E @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ A @ E @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__Some__iff_3) ).

thf(1658,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ E @ B )
       != ( c_Option_Ooption_ONone @ C ) )
      | ( ( hAPP @ ( c_Map_Omap__add @ A @ E @ F @ C ) @ B )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(519,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
       != ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).

thf(2322,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
       != ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
      | ( B = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(186,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).

thf(1538,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)],[186]) ).

thf(682,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/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(2701,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)],[682]) ).

thf(769,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__left__idem_0) ).

thf(2903,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)],[769]) ).

thf(614,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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(2545,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)],[614]) ).

thf(636,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).

thf(2599,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(1084,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

thf(3623,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)],[1084]) ).

thf(250,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) ) @ C ) ) @ D ) ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).

thf(1679,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) ) @ C ) ) @ D ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(956,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(3329,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).

thf(401,axiom,
    ! [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_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).

thf(2044,plain,
    ! [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_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(82,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/sandbox2/benchmark/theBenchmark.p',cls_Int__atLeastAtMost_0) ).

thf(1285,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)],[82]) ).

thf(274,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/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(1738,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)],[274]) ).

thf(832,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ C ) @ D ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).

thf(3041,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ C ) @ D ) @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ B )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(857,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__assoc_0) ).

thf(3095,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)],[857]) ).

thf(356,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/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

thf(1934,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)],[356]) ).

thf(302,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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(1802,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)],[302]) ).

thf(801,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/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(2975,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)],[801]) ).

thf(627,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Map_Odom @ B @ A @ C ) ) @ ( c_Map_Odom @ D @ A @ C ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ( ( c_Map_Omap__add @ B @ D @ A @ C )
        = ( c_Map_Omap__add @ D @ B @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__comm_0) ).

thf(2579,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Map_Odom @ B @ A @ C ) ) @ ( c_Map_Odom @ D @ A @ C ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ( ( c_Map_Omap__add @ B @ D @ A @ C )
        = ( c_Map_Omap__add @ D @ B @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(981,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/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_2) ).

thf(3388,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)],[981]) ).

thf(246,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).

thf(1670,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(750,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Odistrib__lattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

thf(2860,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)],[750]) ).

thf(846,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__subset__iff_1) ).

thf(3071,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(745,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OInf__class_OInf @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).

thf(2848,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OInf__class_OInf @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(495,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).

thf(2266,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)],[495]) ).

thf(629,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

thf(2584,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(669,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/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(2675,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)],[669]) ).

thf(131,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

thf(1404,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)],[131]) ).

thf(112,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).

thf(1358,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(487,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(2247,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)],[487]) ).

thf(555,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ A ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ B ) ) @ v_x )
      = ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__Int__eq_0) ).

thf(2411,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ A ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ B ) ) @ v_x )
      = ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(1024,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/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).

thf(3488,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)],[1024]) ).

thf(594,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

thf(2500,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(188,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(1543,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)],[188]) ).

thf(286,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/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).

thf(1766,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)],[286]) ).

thf(862,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

thf(3107,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)],[862]) ).

thf(431,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/sandbox2/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).

thf(2113,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)],[431]) ).

thf(993,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
        = ( 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/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Ofold1__insert__idem_0) ).

thf(3415,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Finite__Set_Ofold1 @ A @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
        = ( 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)],[993]) ).

thf(25,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).

thf(1141,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(869,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(3124,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(562,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infI2_0) ).

thf(2426,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)],[562]) ).

thf(808,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__le1_0) ).

thf(2992,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)],[808]) ).

thf(376,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

thf(1981,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(258,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).

thf(1702,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(542,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).

thf(2379,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)],[542]) ).

thf(500,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_1) ).

thf(2279,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(533,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/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).

thf(2357,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)],[533]) ).

thf(743,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/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_1) ).

thf(2843,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)],[743]) ).

thf(444,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

thf(2145,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)],[444]) ).

thf(372,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).

thf(1972,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Ooption_ONone @ A )
     != ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(518,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/sandbox2/benchmark/theBenchmark.p',cls_finite__subset_0) ).

thf(2320,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)],[518]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

thf(1749,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(140,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/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

thf(1427,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)],[140]) ).

thf(207,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__greatest_0) ).

thf(1585,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)],[207]) ).

thf(599,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int_0) ).

thf(2511,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(576,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__iff_0) ).

thf(2458,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Oord @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(844,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__mono_0) ).

thf(3067,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)],[844]) ).

thf(887,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(3171,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).

thf(346,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

thf(1913,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)],[346]) ).

thf(1006,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( 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 ) @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_escape_1) ).

thf(3447,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
      | ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( 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 ) @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).

thf(513,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ C @ D @ E @ F @ G ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ C @ D @ E @ F @ G ) @ B ) )
      | ~ ( c_Finite__Set_Ofun__left__comm @ C @ F @ G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_Ofold__graph__determ_0) ).

thf(2310,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ C @ D @ E @ F @ G ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ C @ D @ E @ F @ G ) @ B ) )
      | ~ ( c_Finite__Set_Ofun__left__comm @ C @ F @ G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(1051,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

thf(3548,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).

thf(134,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
        = ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A @ D ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__def_0) ).

thf(1412,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
        = ( c_Finite__Set_Ofold__image @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A @ D ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(641,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Orestrict__map @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ B @ E )
      = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ D @ B @ E ) @ C @ ( hAPP @ A @ C ) @ B @ ( tc_Option_Ooption @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__map__insert_0) ).

thf(2611,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Orestrict__map @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ B @ E )
      = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ D @ B @ E ) @ C @ ( hAPP @ A @ C ) @ B @ ( tc_Option_Ooption @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(293,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

thf(1781,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(661,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).

thf(2658,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(304,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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).

thf(1807,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)],[304]) ).

thf(8,axiom,
    class_Ring__and__Field_Osemiring @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

thf(1108,plain,
    class_Ring__and__Field_Osemiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(1070,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_6) ).

thf(3593,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)],[1070]) ).

thf(752,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_escape_0) ).

thf(2865,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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)],[752]) ).

thf(886,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/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).

thf(3168,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)],[886]) ).

thf(566,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F @ E @ C )
        = ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ A @ F @ E @ C ) @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ ( c_Map_Odom @ F @ E @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__upd__left_0) ).

thf(2435,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F @ E @ C )
        = ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ A @ F @ E @ C ) @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ ( c_Map_Odom @ F @ E @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(936,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 @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__below__iff_2) ).

thf(3284,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 @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ D ) @ B ) )
      | ( 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)],[936]) ).

thf(705,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(2760,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(388,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

thf(2013,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(1019,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) )
        = C )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

thf(3478,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) )
        = C )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(1066,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(3584,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).

thf(875,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( c_Finite__Set_Ofold @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ C @ A @ A ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__eq__fold_0) ).

thf(3139,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( c_Finite__Set_Ofold @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ C @ A @ A ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(348,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
     != ( c_Option_Ooption_ONone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__None__eq_1) ).

thf(1918,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B )
     != ( c_Option_Ooption_ONone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(1010,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

thf(3457,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ 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)],[1010]) ).

thf(95,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).

thf(1316,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)],[95]) ).

thf(1058,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_1) ).

thf(3565,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ 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 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

thf(987,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/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

thf(3401,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)],[987]) ).

thf(153,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).

thf(1459,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(856,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ( ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
        = ( c_Suc @ ( c_Finite__Set_Ocard @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Suc__eq_5) ).

thf(3092,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ( ( c_Finite__Set_Ocard @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
        = ( c_Suc @ ( c_Finite__Set_Ocard @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(754,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(2870,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(736,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ~ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

thf(2828,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
      | ~ ( 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)],[736]) ).

thf(1085,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( c_Finite__Set_Ofold @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__eq__fold_0) ).

thf(3625,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( c_Finite__Set_Ofold @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ C @ A @ A ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).

thf(18,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).

thf(1126,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(699,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Orestrict__map @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ F @ D @ E )
        = ( c_Map_Orestrict__map @ A @ F @ D @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__fun__upd_1) ).

thf(2743,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Orestrict__map @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ ( tc_Option_Ooption @ E ) ) @ F @ D @ E )
        = ( c_Map_Orestrict__map @ A @ F @ D @ E ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(810,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ ( c_HOL_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ tc_bool ) ) ) @ C @ C ) @ F ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ D @ E @ C @ C ) @ F ) )
      | ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__graph__permute__diff_0) ).

thf(2997,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ ( c_HOL_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ tc_bool ) ) ) @ C @ C ) @ F ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ B ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ D @ E @ C @ C ) @ F ) )
      | ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(44,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

thf(1189,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)],[44]) ).

thf(126,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

thf(1390,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)],[126]) ).

thf(511,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
       != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
      | ( B = E )
      | ( C = E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(2305,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
       != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
      | ( B = E )
      | ( C = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(776,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ D @ A @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__le_0) ).

thf(2919,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ D @ A @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(203,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/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

thf(1575,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)],[203]) ).

thf(839,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ C ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__insert_0) ).

thf(3056,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 ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Ofold1 @ ( c_HOL_Oplus__class_Oplus @ A ) @ A ) @ C ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ 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)],[839]) ).

thf(479,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/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_1) ).

thf(2226,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)],[479]) ).

thf(569,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).

thf(2443,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(100,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 ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).

thf(1326,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 ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) ) @ 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)],[100]) ).

thf(634,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ ( c_Option_Oset @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_elem__set_0) ).

thf(2594,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ B ) @ C ) @ ( c_Option_Oset @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(453,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofold @ A @ B @ C @ D @ E )
      = ( c_The @ ( c_Finite__Set_Ofold__graph @ A @ B @ C @ D @ E ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__def_0) ).

thf(2167,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofold @ A @ B @ C @ D @ E )
      = ( c_The @ ( c_Finite__Set_Ofold__graph @ A @ B @ C @ D @ E ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(618,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Max__eqI_1) ).

thf(2554,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( 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)],[618]) ).

thf(174,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).

thf(1508,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(163,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).

thf(1481,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(972,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Option_Oset @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Option_Oset_Osimps_I2_J_0) ).

thf(3369,plain,
    ! [B: $i,A: $i] :
      ( ( c_Option_Oset @ ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ B ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).

thf(277,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Map_Orestrict__map @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ t_a ) @ B @ t_a @ A ) @ v_x )
      = ( c_Option_Ooption_ONone @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__map__empty_0) ).

thf(1745,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Map_Orestrict__map @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ t_a ) @ B @ t_a @ A ) @ v_x )
      = ( c_Option_Ooption_ONone @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(1087,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ B @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ ( c_Map_Odom @ B @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I1_J_0) ).

thf(3630,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
        = ( hAPP @ B @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ E ) @ ( c_Map_Odom @ B @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).

thf(799,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).

thf(2971,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(1037,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/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(3516,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)],[1037]) ).

thf(874,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty_0) ).

thf(3136,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)],[874]) ).

thf(782,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_0) ).

thf(2934,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ A @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(456,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).

thf(2174,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(161,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).

thf(1476,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)],[161]) ).

thf(106,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(1341,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)],[106]) ).

thf(423,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

thf(2098,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(1022,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/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

thf(3484,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)],[1022]) ).

thf(248,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( c_Option_Ooption_ONone @ D ) )
      | ( ( hAPP @ A @ E )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_1) ).

thf(1674,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( c_Option_Ooption_ONone @ D ) )
      | ( ( hAPP @ A @ E )
        = ( c_Option_Ooption_ONone @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(748,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ B @ C ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1 @ B @ A @ C ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__nonempty__imp__fold1Set_0) ).

thf(2855,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ B @ C ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1 @ B @ A @ C ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(747,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/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

thf(2853,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)],[747]) ).

thf(505,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Set_Ovimage @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) ) @ D @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).

thf(2290,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ B ) @ ( c_Set_Ovimage @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) ) @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(728,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ F ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ D @ E @ C @ C ) @ F ) )
      | ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__graph__insert__swap_0) ).

thf(2811,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ E ) @ C @ C ) @ ( hAPP @ ( hAPP @ A @ B ) @ F ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ A @ D @ E @ C @ C ) @ F ) )
      | ~ ( c_OrderedGroup_Oab__semigroup__mult @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(385,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/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

thf(2004,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)],[385]) ).

thf(640,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( 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/sandbox2/benchmark/theBenchmark.p',cls_Min__insert_0) ).

thf(2608,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMin @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( 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)],[640]) ).

thf(564,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(2431,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(1030,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(3501,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(65,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

thf(1244,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)],[65]) ).

thf(708,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(2764,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(572,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OInf__class_OInf @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__binary_0) ).

thf(2447,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OInf__class_OInf @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(792,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(2956,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)],[792]) ).

thf(544,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).

thf(2384,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)],[544]) ).

thf(954,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/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

thf(3324,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)],[954]) ).

thf(722,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/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

thf(2796,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)],[722]) ).

thf(1028,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) )
      = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__restrict_0) ).

thf(3497,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ B @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) )
      = ( c_Fun_Ofun__upd @ ( c_Map_Orestrict__map @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ E @ F @ C @ ( tc_Option_Ooption @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(999,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/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

thf(3430,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)],[999]) ).

thf(535,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_2) ).

thf(2362,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)],[535]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ A @ B @ C @ D )
       != ( c_Map_Omap__add @ B @ A @ C @ D ) )
      | ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_1) ).

thf(1212,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Map_Omap__add @ A @ B @ C @ D )
       != ( c_Map_Omap__add @ B @ A @ C @ D ) )
      | ( c_Map_Omap__le @ A @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(217,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/sandbox2/benchmark/theBenchmark.p',cls_inf__min_0) ).

thf(1607,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)],[217]) ).

thf(242,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).

thf(1661,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(516,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ D @ A @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__less__iff__gr__or__eq_1) ).

thf(2315,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ D @ A @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(591,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(2494,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(646,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infE_1) ).

thf(2623,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)],[646]) ).

thf(715,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_1) ).

thf(2779,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)],[715]) ).

thf(773,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

thf(2912,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(400,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( F = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_0) ).

thf(2041,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) @ E @ ( tc_Option_Ooption @ C ) ) @ F )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( ( hAPP @ A @ F )
        = ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ G ) )
      | ( F = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(928,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( 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/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).

thf(3267,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( 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)],[928]) ).

thf(578,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).

thf(2462,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(1042,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ D @ A ) @ ( hAPP @ B @ E ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1__ring_0) ).

thf(3529,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ D @ A ) @ ( hAPP @ B @ E ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).

thf(260,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).

thf(1706,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(964,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/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(3351,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)],[964]) ).

thf(176,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/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

thf(1513,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)],[176]) ).

thf(398,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) ) @ C ) ) @ D )
        = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).

thf(2036,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 ) @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) ) @ C ) ) @ D )
        = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(92,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).

thf(1309,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(381,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).

thf(1994,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(1053,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).

thf(3552,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).

thf(34,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/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).

thf(1161,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)],[34]) ).

thf(220,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).

thf(1614,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ 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)],[220]) ).

thf(290,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).

thf(1774,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 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(80,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

thf(1280,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)],[80]) ).

thf(204,axiom,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_Orderings_Olinorder @ ( c_COMBC @ ( c_lessequals @ A ) @ A @ A @ tc_bool ) @ ( c_COMBC @ ( c_HOL_Oord__class_Oless @ A ) @ A @ A @ tc_bool ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dual__linorder_0) ).

thf(1578,plain,
    ! [A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_Orderings_Olinorder @ ( c_COMBC @ ( c_lessequals @ A ) @ A @ A @ tc_bool ) @ ( c_COMBC @ ( c_HOL_Oord__class_Oless @ A ) @ A @ A @ tc_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(804,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/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).

thf(2983,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)],[804]) ).

thf(225,axiom,
    class_Orderings_Obot @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

thf(1625,plain,
    class_Orderings_Obot @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(927,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( 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/sandbox2/benchmark/theBenchmark.p',cls_Max__insert_0) ).

thf(3264,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
        = ( 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)],[927]) ).

thf(790,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ B @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ D )
      | ( ( c_Finite__Set_Osetprod @ B @ E @ D @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__zero__iff_2) ).

thf(2951,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ B @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ D )
      | ( ( c_Finite__Set_Osetprod @ B @ E @ D @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(331,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Fun_Ofun__upd @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ E ) @ F @ ( tc_Option_Ooption @ D ) ) @ F @ D )
      = ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ A @ B @ F @ D ) @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ E ) @ F @ ( tc_Option_Ooption @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__upd_0) ).

thf(1876,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ A @ ( c_Fun_Ofun__upd @ B @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ E ) @ F @ ( tc_Option_Ooption @ D ) ) @ F @ D )
      = ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ A @ B @ F @ D ) @ C @ ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ E ) @ F @ ( tc_Option_Ooption @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(959,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/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(3337,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)],[959]) ).

thf(872,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/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(3132,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)],[872]) ).

thf(283,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).

thf(1757,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)],[283]) ).

thf(1015,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ A @ tc_bool ) ) )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

thf(3469,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ A @ tc_bool ) ) )
      = ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).

thf(443,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).

thf(2142,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)],[443]) ).

thf(977,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(3379,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Finite__Set_Olattice__class_OInf__fin @ A )
        = ( c_Finite__Set_Ofold1 @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__fin__def__raw_0) ).

thf(1116,plain,
    ! [A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Finite__Set_Olattice__class_OInf__fin @ A )
        = ( c_Finite__Set_Ofold1 @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(344,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ A @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ B @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__SomeD_1) ).

thf(1908,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ C @ D ) @ E )
       != ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ A @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) )
      | ( ( hAPP @ B @ E )
        = ( hAPP @ ( c_Option_Ooption_OSome @ D ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(476,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(2218,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)],[476]) ).

thf(492,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

thf(2258,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(510,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ ( c_Map_Odom @ A @ E @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domI_0) ).

thf(2302,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ B ) @ ( c_Map_Odom @ A @ E @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(673,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(2683,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) @ D @ A )
        = ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).

thf(1229,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ B ) @ C ) @ D @ A )
        = ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omax @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(482,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Ominus @ A )
      | ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).

thf(2233,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_HOL_Ominus @ A )
      | ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
        = ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(605,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__Un_0) ).

thf(2522,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)],[605]) ).

thf(859,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/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(3100,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)],[859]) ).

thf(1013,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/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

thf(3464,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)],[1013]) ).

thf(121,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/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).

thf(1380,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)],[121]) ).

thf(730,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ A @ B @ C @ D ) ) @ ( c_Map_Odom @ A @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__def_1) ).

thf(2815,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ A @ B @ C @ D )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ C ) @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ A @ B @ C @ D ) ) @ ( c_Map_Odom @ A @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(378,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).

thf(1986,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)],[378]) ).

thf(877,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).

thf(3145,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(818,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_5) ).

thf(3015,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)],[818]) ).

thf(144,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

thf(1436,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)],[144]) ).

thf(379,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/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).

thf(1989,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)],[379]) ).

thf(523,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

thf(2334,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(933,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageD_0) ).

thf(3277,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( hAPP @ B @ C ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ E ) @ C ) @ ( c_Set_Ovimage @ B @ D @ E @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).

thf(890,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(3177,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(700,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ A ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ B ) ) @ v_x )
      = ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__Un__eq_0) ).

thf(2746,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ A ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ B ) ) @ v_x )
      = ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(774,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/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(2913,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)],[774]) ).

thf(644,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).

thf(2619,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
      = ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(1032,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/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infI_0) ).

thf(3506,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)],[1032]) ).

thf(658,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Olattice__class_OInf__fin @ A ) @ C ) )
        = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__Inf__absorb_0) ).

thf(2651,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( c_Finite__Set_Olattice__class_OInf__fin @ A ) @ C ) )
        = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(616,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(2549,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)],[616]) ).

thf(702,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ B @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ D )
      | ( ( c_Finite__Set_Osetprod @ B @ E @ D @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__zero_0) ).

thf(2751,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ B @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ C ) @ E ) )
      | ~ ( c_Finite__Set_Ofinite @ E @ D )
      | ( ( c_Finite__Set_Osetprod @ B @ E @ D @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(724,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/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Omult__left__idem_0) ).

thf(2800,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)],[724]) ).

thf(307,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

thf(1816,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)],[307]) ).

thf(169,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 ) @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) ) @ C ) ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).

thf(1495,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 ) @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) ) @ C ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(104,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( c_Finite__Set_Ofinite @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__infinite_0) ).

thf(1335,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_Finite__Set_Osetsum @ B @ C @ D @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( c_Finite__Set_Ofinite @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(255,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).

thf(1693,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(794,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ E ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ A @ A ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__graph__insert__swap_0) ).

thf(2961,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ E ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Oplus__class_Oplus @ A ) @ C @ D @ A @ A ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(83,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/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).

thf(1288,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)],[83]) ).

thf(262,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__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 ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).

thf(1710,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__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 ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(997,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/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_1) ).

thf(3426,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)],[997]) ).

thf(337,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/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

thf(1891,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)],[337]) ).

thf(160,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

thf(1473,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)],[160]) ).

thf(1088,axiom,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
        = ( hAPP @ ( hAPP @ E @ C ) @ D ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).

thf(3633,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
        = ( hAPP @ ( hAPP @ E @ C ) @ D ) )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).

thf(409,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/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).

thf(2063,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)],[409]) ).

thf(218,axiom,
    class_Orderings_Opreorder @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(1610,plain,
    class_Orderings_Opreorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(436,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

thf(2127,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)],[436]) ).

thf(72,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__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 ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).

thf(1261,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__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 ) @ B ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(75,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ A @ D @ C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_upd__None__map__le_0) ).

thf(1268,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ A @ D @ C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(29,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ ( c_Fun_Ofun__upd @ E @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ F ) @ D @ ( tc_Option_Ooption @ C ) ) @ D @ C )
      | ~ ( c_Map_Omap__le @ A @ E @ D @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__imp__upd__le_0) ).

thf(1152,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ A @ B @ ( c_Option_Ooption_ONone @ C ) @ D @ ( tc_Option_Ooption @ C ) ) @ ( c_Fun_Ofun__upd @ E @ B @ ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ F ) @ D @ ( tc_Option_Ooption @ C ) ) @ D @ C )
      | ~ ( c_Map_Omap__le @ A @ E @ D @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(968,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).

thf(3360,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) @ B )
      | ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).

thf(206,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

thf(1582,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)],[206]) ).

thf(580,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/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).

thf(2467,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)],[580]) ).

thf(925,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 @ B @ C @ A ) ) @ B ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__eqI_0) ).

thf(3259,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( hAPP @ ( c_Finite__Set_Olinorder__class_OMax @ A ) @ B )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 @ B @ C @ A ) ) @ B ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).

thf(597,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__empty_0) ).

thf(2507,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)],[597]) ).

thf(539,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).

thf(2372,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)],[539]) ).

thf(441,axiom,
    class_Lattices_Olower__semilattice @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).

thf(2138,plain,
    class_Lattices_Olower__semilattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(354,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).

thf(1930,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(531,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

thf(2353,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(449,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/sandbox2/benchmark/theBenchmark.p',cls_less__infI2_0) ).

thf(2159,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)],[449]) ).

thf(969,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).

thf(3362,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(110,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

thf(1352,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)],[110]) ).

thf(313,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/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(1829,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)],[313]) ).

thf(374,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

thf(1977,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)],[374]) ).

thf(19,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).

thf(1129,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)],[19]) ).

thf(725,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(2803,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(184,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).

thf(1532,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)],[184]) ).

thf(767,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Orderings_Olinorder @ A @ B @ C )
      | ( ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) ) )
        = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_OMax__singleton_0) ).

thf(2898,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Orderings_Olinorder @ A @ B @ C )
      | ( ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ E ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) ) )
        = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).

thf(1384,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(587,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/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(2485,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)],[587]) ).

thf(171,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(1500,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(350,axiom,
    class_HOL_Ominus @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).

thf(1923,plain,
    class_HOL_Ominus @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(919,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(3245,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).

thf(212,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).

thf(1597,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)],[212]) ).

thf(333,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).

thf(1880,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)],[333]) ).

thf(142,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/sandbox2/benchmark/theBenchmark.p',cls_setsum__Un__Int_0) ).

thf(1431,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)],[142]) ).

thf(335,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

thf(1885,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(681,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).

thf(2699,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)],[681]) ).

thf(1027,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Olattice_OInf__fin @ A @ B @ C )
        = ( hAPP @ D @ B ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ E @ F @ G @ A @ H @ I @ J @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__fin__Inf_0) ).

thf(3494,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Finite__Set_Olattice_OInf__fin @ A @ B @ C )
        = ( hAPP @ D @ B ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ~ ( c_Finite__Set_Ofinite @ B @ C )
      | ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ E @ F @ G @ A @ H @ I @ J @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).

thf(173,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).

thf(1505,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)],[173]) ).

thf(129,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).

thf(1399,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)],[129]) ).

thf(703,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/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(2754,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)],[703]) ).

thf(758,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ C @ D @ A @ A ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph__insert__swap_0) ).

thf(2879,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ A ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ ( c_HOL_Otimes__class_Otimes @ A ) @ C @ D @ A @ A ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(1002,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/sandbox2/benchmark/theBenchmark.p',cls_setsum__Un__disjoint_0) ).

thf(3437,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)],[1002]) ).

thf(759,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OBODY @ A )
     != ( c_Com_Ocom_OSemi @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).

thf(2881,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Com_Ocom_OBODY @ A )
     != ( c_Com_Ocom_OSemi @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(470,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/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).

thf(2206,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)],[470]) ).

thf(390,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ t_a @ C ) @ v_x )
      = ( c_Option_Ooption_Ooption__case @ ( hAPP @ A @ v_x ) @ ( c_Option_Ooption_OSome @ C ) @ ( hAPP @ B @ v_x ) @ ( tc_Option_Ooption @ C ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__def_0) ).

thf(2018,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_Map_Omap__add @ A @ B @ t_a @ C ) @ v_x )
      = ( c_Option_Ooption_Ooption__case @ ( hAPP @ A @ v_x ) @ ( c_Option_Ooption_OSome @ C ) @ ( hAPP @ B @ v_x ) @ ( tc_Option_Ooption @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(320,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ G @ D @ E )
        = ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ F @ G @ D @ E ) @ B @ C @ D @ E ) )
      | ( B = F ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).

thf(1848,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)],[320]) ).

thf(1000,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__card__mono_0) ).

thf(3432,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)],[1000]) ).

thf(643,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OBODY @ A )
       != ( c_Com_Ocom_OBODY @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).

thf(2615,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Com_Ocom_OBODY @ A )
       != ( c_Com_Ocom_OBODY @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(837,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/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

thf(3052,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)],[837]) ).

thf(419,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).

thf(2087,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(941,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).

thf(3296,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)],[941]) ).

thf(458,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/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

thf(2177,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)],[458]) ).

thf(817,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/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

thf(3013,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)],[817]) ).

thf(1041,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ D @ A ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ C @ D @ E ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv1_0) ).

thf(3526,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( hAPP @ D @ A ) @ B ) )
      | ~ ( c_Orderings_Olinorder @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

thf(1012,axiom,
    ! [A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__empty_0) ).

thf(3461,plain,
    ! [A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).

thf(97,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).

thf(1320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(360,axiom,
    class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

thf(1944,plain,
    class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(116,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/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).

thf(1367,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)],[116]) ).

thf(361,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

thf(1945,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)],[361]) ).

thf(943,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(3299,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(251,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/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).

thf(1681,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)],[251]) ).

thf(989,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/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

thf(3405,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)],[989]) ).

thf(414,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/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

thf(2074,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)],[414]) ).

thf(677,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 @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1_H_0) ).

thf(2690,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 @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ D ) @ E ) @ C ) )
      | ~ ( c_Finite__Set_Ofinite @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(198,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ B @ A )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__map__add_0) ).

thf(1565,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Map_Omap__add @ ( c_COMBK @ ( c_Option_Ooption_ONone @ A ) @ ( tc_Option_Ooption @ A ) @ B ) @ C @ B @ A )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(567,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/sandbox2/benchmark/theBenchmark.p',cls_finite__UnI_0) ).

thf(2438,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)],[567]) ).

thf(167,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).

thf(1490,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(508,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

thf(2297,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)],[508]) ).

thf(1004,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(3443,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
      = ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).

thf(149,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/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

thf(1449,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)],[149]) ).

thf(306,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).

thf(1812,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)],[306]) ).

thf(835,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
      = ( c_HOL_Ominus__class_Ominus @ ( 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 ) @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

thf(3047,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
      = ( c_HOL_Ominus__class_Ominus @ ( 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 ) @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(581,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Map_Odom @ A @ E @ C ) )
        = ( c_Map_Odom @ A @ E @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__dom_0) ).

thf(2470,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ A @ B )
       != ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ D ) )
      | ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ ( c_Map_Odom @ A @ E @ C ) )
        = ( c_Map_Odom @ A @ E @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(803,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__Un_0) ).

thf(2980,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)],[803]) ).

thf(829,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/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

thf(3035,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)],[829]) ).

thf(3664,plain,
    $false,
    inference(e,[status(thm)],[2452,1469,3399,3434,2921,2787,2480,3021,1322,1665,2822,2630,1369,2889,1168,2295,3345,2341,2336,3008,1633,2778,2072,3661,1559,1105,2876,1237,2559,3449,1179,2331,1818,1295,1956,1549,1554,1110,3172,3185,1158,2940,3317,1290,2231,2381,1618,3098,1728,1205,1793,3382,1855,1200,3534,1924,2210,2808,2644,2395,2908,1443,2776,2659,2527,3040,3153,2590,1401,2947,1939,2099,1591,2837,1269,1173,1486,1655,3049,2686,3616,2476,3577,2360,2195,3017,1788,3217,3004,3332,3367,3365,2740,3044,1735,2184,3175,3121,3481,3562,1640,2901,3313,3335,1835,2216,2046,2985,2020,3088,2010,2886,2082,2516,2348,3545,2723,2491,1782,3249,1441,1650,1645,1921,1386,3281,3466,1967,2067,2825,2136,1904,1265,2531,2405,1623,3597,3221,3644,2735,1298,2667,2339,3342,3061,2708,1313,2562,2571,2703,2654,1628,1409,3204,2603,2916,3195,3029,2039,3275,1871,3574,3617,1330,2444,1860,3612,3653,1511,2274,2682,1826,3410,2185,1455,1832,2897,1191,1992,3353,1462,1132,3043,1800,2713,3374,1147,1704,2767,1479,2730,2024,3180,3602,3231,1100,1232,1545,2420,2169,2403,3638,1247,2049,1347,1572,1741,3084,2989,1362,1963,2388,2533,2007,3199,1911,3473,1136,1858,2925,3290,1489,2950,1415,1302,2794,1714,2027,2105,3075,2090,3393,1109,2893,1632,1418,2236,3357,2254,3569,1677,2034,1377,1215,2483,1796,1526,2002,2103,3226,2965,1843,2058,2367,3537,2833,3189,2281,2190,3421,1119,2424,2772,3157,2242,2286,2639,3588,1104,3559,3606,3211,2154,1521,3492,2718,2586,2884,1975,3510,2762,3378,1863,2954,3582,3459,3301,2473,3567,2574,2646,1306,2164,2118,1338,2737,2641,3418,3591,2910,1915,1708,2093,1311,3054,2496,2621,2790,2660,1768,1868,2061,3550,2000,1730,3037,1163,1223,2249,2541,1519,1255,1123,1570,1217,1751,3069,3371,3134,1824,2032,2132,3514,2015,1274,2673,2705,2264,1900,1723,2601,2428,2733,2805,2277,1355,1580,3471,1883,1602,2433,1951,1888,2200,2179,1159,2345,1407,2228,3647,1106,1423,3307,3271,2445,3191,2464,2873,1365,2628,2670,3403,2565,2663,1555,2820,3499,3065,3556,3600,1687,1457,2547,2313,3033,3408,3595,2769,3445,3105,2377,1953,2895,2577,1111,1425,3650,3237,3001,3018,1360,2245,2498,1541,3254,3413,1851,1772,1259,3122,2841,1328,2973,1121,1498,1587,2509,3102,1672,1878,3386,1138,2724,1719,2858,2268,3440,1567,3326,1942,3622,2053,3428,2649,2781,2460,1493,2798,2830,1182,3010,2455,2613,1937,2108,1446,2551,1207,2317,3294,3242,1324,3540,1984,2813,1720,3215,1776,1263,3656,2450,3486,1099,1249,2519,3126,3541,1530,1382,2487,2845,3059,1552,2851,2355,1932,2505,3390,3628,3115,1429,3247,2862,1599,2697,3109,1979,3162,1759,1393,3476,1318,2203,1779,2208,3279,1695,1466,2440,2221,3508,1616,2529,1732,3147,3454,2634,1434,1241,2761,1846,1712,3306,2076,2748,1170,2963,3321,2408,1663,2121,1906,2936,2413,1754,1103,3257,1483,1747,3262,3523,1374,2677,2176,2524,3396,1154,3187,2727,3504,3519,3609,2188,1388,1535,2398,3604,1965,2817,2134,2970,3319,3636,3234,2938,2791,3240,1620,2489,2393,3086,1652,1929,1226,2695,1256,2959,3213,3118,2293,1635,1107,1332,2055,3304,2148,3532,3223,2161,1139,1503,2193,3023,2029,2326,2891,1271,2308,1371,3077,3208,1865,3340,1239,1997,3619,3579,1897,2557,3641,3091,1464,1638,3355,1194,2079,2521,2679,1574,2906,1144,3197,3384,1439,2065,1209,2721,2538,1853,1282,2478,3251,2151,3155,2084,2214,2415,1894,2987,2637,2422,2774,3287,1524,1349,3270,1589,2284,1603,2299,2116,2839,2943,2945,3586,1690,3182,2197,1969,1667,2182,1471,2632,1630,3572,2757,3165,1556,2252,1293,2928,1112,3219,2824,2605,3027,2314,2129,2343,2625,2111,3073,2261,1821,2923,1838,3614,3006,3451,1149,3298,2874,3483,1344,3150,2329,2710,1820,2350,2835,1528,1643,2139,1176,1113,2592,3142,3512,2693,1805,3539,2418,1198,1841,1396,1926,2365,1699,2401,1594,2212,2171,2051,3423,3159,2369,2931,2288,2022,3310,2535,2101,1726,2967,2390,2999,3348,2156,2069,2867,3490,1562,1948,2239,3031,1809,2096,1203,2665,1420,1134,2684,2256,3292,2582,1626,3522,1304,1873,3193,1166,2107,1467,2994,2784,2271,3206,2503,1684,1277,2124,2597,1958,2513,1547,2715,1961,3112,1743,3082,1647,3659,1252,3129,2518,3228,1798,3391,1770,3376,1516,3315,2977,1611,2375,1156,1605,2588,1753,2386,2569,2165,3063,1186,3554,3202,1785,3026,1235,1763,1220,2656,3019,3080,1790,1716,2224,1300,1452,1637,2688,3273,1901,3544,1658,2322,1538,2701,2903,2545,2599,3623,1679,3329,2044,1285,1738,3041,3095,1934,1802,2975,2579,3388,1670,2860,3071,2848,2266,2584,2675,1404,1358,2247,2411,3488,2500,1543,1766,3107,2113,3415,1141,3124,2426,2992,1981,1702,2379,2279,2357,2843,2145,1972,2320,1749,1427,1585,2511,2458,3067,3171,1913,3447,2310,3548,1412,2611,1781,2658,1807,1108,3593,2865,3168,2435,3284,2760,2013,3478,3584,3139,1918,3457,1316,3565,3401,1459,3092,2870,2828,3625,1126,2743,2997,1189,1390,2305,2919,1575,3056,2226,2443,1326,2594,2167,2554,1508,1481,3369,1745,3630,2971,3516,3136,2934,2174,1476,1341,2098,3484,1674,2855,2853,2290,2811,2004,2608,2431,3501,1244,2764,2447,2956,2384,3324,2796,3497,3430,2362,1212,1607,1661,2315,2494,2623,2779,2912,2041,3267,2462,3529,1706,3351,1513,2036,1309,1994,3552,1161,1614,1774,1280,1578,2983,1625,3264,2951,1876,3337,3132,1757,3469,2142,3379,1116,1908,2218,2258,2302,2683,1229,2233,2522,3100,3464,1380,2815,1986,3145,3015,1436,1989,2334,3277,3177,2746,2913,2619,3506,2651,2549,2751,2800,1816,1495,1335,1693,2961,1288,1710,3426,1891,1473,3633,2063,1610,2127,1261,1268,1152,3360,1582,2467,3259,2507,2372,2138,1930,2353,2159,3362,1352,1829,1977,1129,2803,1532,2898,1384,2485,1500,1923,3245,1597,1880,1431,1885,2699,3494,1505,1399,2754,2879,3437,2881,2206,2018,1848,3432,2615,3052,2087,3296,2177,3013,3526,3461,1320,1944,1367,1945,3299,1681,3405,2074,2690,1565,2438,1490,2297,3443,1449,1812,3047,2470,2980,3035]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV875-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n027.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Fri May 19 03:10:22 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.95/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.84/1.09  % [INFO] 	 Parsing done (250ms). 
% 1.84/1.10  % [INFO] 	 Running in sequential loop mode. 
% 2.41/1.29  % [INFO] 	 eprover registered as external prover. 
% 2.41/1.29  % [INFO] 	 cvc4 registered as external prover. 
% 2.41/1.30  % [INFO] 	 Scanning for conjecture ... 
% 2.87/1.44  % [INFO] 	 Found a conjecture and 1106 axioms. Running axiom selection ... 
% 3.61/1.65  % [INFO] 	 Axiom selection finished. Selected 1096 axioms (removed 10 axioms). 
% 4.64/1.90  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.64/1.92  % [INFO] 	 Type checking passed. 
% 4.64/1.93  % [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 ... 
% 14.86/4.40  % External prover 'e' found a proof!
% 14.86/4.40  % [INFO] 	 Killing All external provers ... 
% 14.86/4.40  % Time passed: 3881ms (effective reasoning time: 3291ms)
% 14.86/4.40  % 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)>
% 14.94/4.40  % Axioms used in derivation (1096): cls_inf__sup__aci_I2_J_0, cls_the__sym__eq__trivial_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_add__pos__nonneg_0, cls_subset__insert_1, cls_Diff__iff_2, cls_restrict__map__to__empty_0, cls_Min__insert_0, cls_set__empty__eq_1, cls_bot__fun__eq_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, 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_option_Oinject_0, cls_map__le__upd_0, cls_ab__semigroup__mult_Omult__left__commute_0, cls_mult__less__cancel__left__disj_5, cls_less__iff__diff__less__0_0, cls_atLeastatMost__subset__iff_2, cls_Diff__cancel_0, cls_min__max_Oinf__commute_0, cls_map__upd__eqD1_0, cls_add__0__left_0, cls_Int__absorb2_0, cls_com_Osimps_I18_J_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_mult__zero__right_0, cls_sup__ge1_0, clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite, cls_mult__nonneg__nonneg_0, cls_less__fun__def_1, 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_insert__inter__insert_0, cls_lower__semilattice_Oinf__left__idem_0, cls_min__max_Osup__inf__distrib1_0, cls_map__add__None_2, cls_add__less__cancel__left_1, cls_mult__right__mono_0, cls_insertE_0, cls_Un__subset__iff_0, cls_Suc__inject_0, cls_setsum__diff_0, cls_subset__empty_1, cls_mult__nonneg__nonpos2_0, cls_map__add__assoc_0, cls_sum__squares__eq__zero__iff_0, cls_min__max_Oinf__sup__distrib1_0, cls_Suc__n__not__n_0, cls_fun__left__comm_Ofold__fun__comm_0, cls_min__max_Ole__sup__iff_2, cls_min__less__iff__conj_0, cls_Un__empty__left_0, cls_map__upd__Some__unfold_4, cls_le__funD_0, cls_atLeastatMost__psubset__iff_2, cls_setprod__Un__Int_0, cls_setsum__0_0, cls_xt1_I12_J_0, cls_weak__Body_0, cls_COMBC__def_0, cls_mult__less__cancel__right__disj_0, cls_ab__semigroup__mult_Ofold1__Un_0, cls_finite__insert_0, cls_fold1__eq__fold__idem_0, cls_min__max_Oinf__le1_0, cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_mult__less__cancel__left__disj_1, cls_sup__bot__right_0, cls_fold1__insert_0, cls_insert__code_1, cls_map__le__trans_0, cls_fun__upd__apply_1, clsarity_nat__Lattices_Odistrib__lattice, cls_add__increasing2_0, cls_card__insert_0, cls_Int__atLeastAtMost_0, cls_zero__le__mult__iff_3, cls_less__antisym_0, cls_Un__upper1_0, cls_fold1Set__sing_1, cls_Un__commute_0, cls_lower__semilattice_Oinf__commute_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_pos__add__strict_0, cls_UnCI_1, cls_class__semiring_Osemiring__rules_I21_J_0, cls_dual__semilattice_0, cls_setsum__Un_0, clsarity_bool__Lattices_Olower__semilattice, cls_map__upd__Some__unfold_3, cls_distrib__sup__le_0, cls_Int__mono_0, cls_fun__left__comm_Ofun__left__comm_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_comm__monoid__add_Ofun__left__comm_0, cls_le__iff__inf_1, cls_complete__lattice_OSup__singleton_0, cls_conseq_0, cls_inf__sup__aci_I6_J_0, cls_restrict__fun__upd_0, cls_lower__semilattice_Oab__semigroup__idem__mult__inf_0, cls_lower__semilattice_Ole__inf__iff_0, cls_Option_Oset_Osimps_I2_J_0, clsarity_fun__Orderings_Oorder, cls_not__sum__squares__lt__zero_0, cls_finite__Un_2, cls_COMBK__def_0, cls_min__max_Osup__inf__absorb_0, cls_add__le__cancel__left_1, cls_Int__insert__left_0, cls_triple_Oinject_1, cls_add__imp__eq_0, cls_min__less__iff__disj_2, cls_option_Osimps_I2_J_0, cls_add__le__cancel__right_1, cls_linorder_Onot__less__iff__gr__or__eq_2, clsarity_nat__Orderings_Olinorder, cls_setprod__diff1_1, 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% 14.94/4.40  % No. of inferences in proof: 2197
% 14.94/4.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3881 ms resp. 3291 ms w/o parsing
% 16.04/4.82  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.34/4.83  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------