Leo-III---1.8.0.UNS-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV875-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 09:00:52 AM UTC 2026

% Result   : Unsatisfiable 26.92s 7.59s
% Output   : Refutation 30.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      : 1098
% Syntax   : Number of formulae    : 2197 ( 395 unt;   0 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  :    0 (   0   >;   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_decl,type,
    hBOOL: $i > $o ).

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

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

thf(c_Com_Ocom_OSKIP_decl,type,
    c_Com_Ocom_OSKIP: $i ).

thf(v_x_decl,type,
    v_x: $i ).

thf(c_Hoare__Mirabelle_Ohoare__derivs_decl,type,
    c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).

thf(v_G_decl,type,
    v_G: $i ).

thf(c_Set_Oinsert_decl,type,
    c_Set_Oinsert: $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(class_Ring__and__Field_Ocomm__semiring__1_decl,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

thf(c_HOL_Oplus__class_Oplus_decl,type,
    c_HOL_Oplus__class_Oplus: $i > $i ).

thf(class_Lattices_Olattice_decl,type,
    class_Lattices_Olattice: $i > $o ).

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

thf(c_Finite__Set_Ofold1_decl,type,
    c_Finite__Set_Ofold1: $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

thf(class_OrderedGroup_Ocancel__ab__semigroup__add_decl,type,
    class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).

thf(class_Orderings_Olinorder_decl,type,
    class_Orderings_Olinorder: $i > $o ).

thf(c_Orderings_Oord__class_Omin_decl,type,
    c_Orderings_Oord__class_Omin: $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_OrderedGroup_Oab__semigroup__idem__mult_decl,type,
    c_OrderedGroup_Oab__semigroup__idem__mult: $i > $i > $o ).

thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).

thf(class_OrderedGroup_Olordered__ab__group__add__join_decl,type,
    class_OrderedGroup_Olordered__ab__group__add__join: $i > $o ).

thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

thf(class_Orderings_Oorder_decl,type,
    class_Orderings_Oorder: $i > $o ).

thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
    class_OrderedGroup_Olordered__ab__group__add: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(class_Orderings_Opreorder_decl,type,
    class_Orderings_Opreorder: $i > $o ).

thf(class_Orderings_Obot_decl,type,
    class_Orderings_Obot: $i > $o ).

thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_decl,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

thf(class_Ring__and__Field_Omult__mono1_decl,type,
    class_Ring__and__Field_Omult__mono1: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_Option_Oset_decl,type,
    c_Option_Oset: $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3_decl,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_decl,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_decl,type,
    c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1: $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq12__1_decl,type,
    v_sko__Hoare__Mirabelle__Xconseq12__1: $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq12__2_decl,type,
    v_sko__Hoare__Mirabelle__Xconseq12__2: $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq2__1_decl,type,
    v_sko__Hoare__Mirabelle__Xconseq2__1: $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq2__2_decl,type,
    v_sko__Hoare__Mirabelle__Xconseq2__2: $i > $i > $i ).

thf(c_Finite__Set_Ocard_decl,type,
    c_Finite__Set_Ocard: $i > $i > $i ).

thf(c_Finite__Set_Ofold1Set_decl,type,
    c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1_decl,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_decl,type,
    v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1: $i > $i > $i > $i > $i ).

thf(c_Nitpick_Ofold__graph_H_decl,type,
    c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).

thf(t_b_decl,type,
    t_b: $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq1__1_decl,type,
    v_sko__Hoare__Mirabelle__Xconseq1__1: $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq1__2_decl,type,
    v_sko__Hoare__Mirabelle__Xconseq1__2: $i > $i > $i ).

thf(c_Nitpick_Osko__Nitpick__XEx1__def__1__3_decl,type,
    c_Nitpick_Osko__Nitpick__XEx1__def__1__3: $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xconseq12__3_decl,type,
    v_sko__Hoare__Mirabelle__Xconseq12__3: $i > $i > $i > $i > $i ).

thf(c_Map_Osko__Map__Xmap__le__def__1__1_decl,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_decl,type,
    c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1: $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xescape__1_decl,type,
    v_sko__Hoare__Mirabelle__Xescape__1: $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xescape__2_decl,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_decl,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_decl,type,
    c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2: $i > $i > $i ).

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

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

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

thf(c_Hoare__Mirabelle_Ohoare__valids_decl,type,
    c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).

thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3_decl,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_decl,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_decl,type,
    v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1: $i > $i > $i > $i > $i ).

thf(c_Finite__Set_Olattice_OInf__fin_decl,type,
    c_Finite__Set_Olattice_OInf__fin: $i > $i > $i > $i ).

thf(c_Map_Osko__Map__XdomD__1__1_decl,type,
    c_Map_Osko__Map__XdomD__1__1: $i > $i > $i > $i > $i ).

thf(449,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI2_0) ).

thf(2163,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(265,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

thf(1718,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(420,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).

thf(2094,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(639,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oless__linear_0) ).

thf(2612,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

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

thf(1633,plain,
    tc_nat @ class_Ring__and__Field_Omult__mono1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(1095,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(3661,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).

thf(983,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).

thf(3399,plain,
    ! [A: $i] :
      ( ( A @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).

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

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

thf(576,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__iff_0) ).

thf(2463,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(560,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

thf(2427,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

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

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

thf(466,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

thf(2199,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(817,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

thf(3021,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

thf(207,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__greatest_0) ).

thf(1586,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(171,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(1501,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(572,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__binary_0) ).

thf(2452,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(759,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Com_Ocom_OBODY )
     != ( C @ ( B @ c_Com_Ocom_OSemi ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).

thf(2889,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ c_Com_Ocom_OBODY )
     != ( C @ ( B @ c_Com_Ocom_OSemi ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(44,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

thf(1190,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

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

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

thf(510,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( E @ ( A @ c_Map_Odom ) ) @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domI_0) ).

thf(2306,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( E @ ( A @ c_Map_Odom ) ) @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(959,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(3345,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

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

thf(2341,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = D )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

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

thf(2336,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(427,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).

thf(2109,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(436,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

thf(2131,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

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

thf(2031,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
      = ( E @ ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__add ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(997,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ ( B @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_1) ).

thf(3434,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ ( B @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).

thf(883,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__Diff__lessThan_0) ).

thf(3167,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(774,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(2921,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(1015,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

thf(3477,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).

thf(715,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_1) ).

thf(2787,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(631,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( F @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( E @ ( tc_bool @ ( F @ tc_fun ) @ ( tc_bool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Nitpick_Ofold__graph_H ) ) ) ) ) )
      | ( G @ ( F @ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Nitpick_Ofold__graph_H ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I2_J_0) ).

thf(2595,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( F @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( E @ ( tc_bool @ ( F @ tc_fun ) @ ( tc_bool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( F @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Nitpick_Ofold__graph_H ) ) ) ) ) )
      | ( G @ ( F @ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Nitpick_Ofold__graph_H ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(319,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice ) ) ) )
      | ( B @ ( A @ c_OrderedGroup_Oab__semigroup__idem__mult ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oab__semigroup__idem__mult__inf_0) ).

thf(1850,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice ) ) ) )
      | ( B @ ( A @ c_OrderedGroup_Oab__semigroup__idem__mult ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(591,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(2499,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

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

thf(1179,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(520,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Finite__Set_Osetsum ) ) ) )
        = ( tc_nat @ ( C @ ( B @ ( A @ c_Finite__Set_Osetsum ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1__nat_1) ).

thf(2331,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Finite__Set_Osetsum ) ) ) )
        = ( tc_nat @ ( C @ ( B @ ( A @ c_Finite__Set_Osetsum ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(890,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(3185,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(470,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).

thf(2210,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(431,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).

thf(2117,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(332,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(1882,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(643,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Com_Ocom_OBODY )
       != ( B @ c_Com_Ocom_OBODY ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).

thf(2622,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Com_Ocom_OBODY )
       != ( B @ c_Com_Ocom_OBODY ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(787,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__empty_0) ).

thf(2953,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

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

thf(3012,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(75,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( A @ ( C @ tc_Option_Ooption @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__le ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_upd__None__map__le_0) ).

thf(1269,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( D @ ( A @ ( C @ tc_Option_Ooption @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__le ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(90,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).

thf(1305,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(144,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

thf(1437,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

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

thf(3382,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).

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

thf(321,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).

thf(1855,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(1041,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Olinorder ) ) )
      | ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv1_0) ).

thf(3534,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ c_Orderings_Olinorder ) ) )
      | ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

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

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

thf(511,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = E )
      | ( B = E )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(2309,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = E )
      | ( B = E )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(597,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__empty_0) ).

thf(2512,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(724,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Omult__left__idem_0) ).

thf(2808,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

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

thf(1522,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( F @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(547,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).

thf(2395,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
     != c_Com_Ocom_OSKIP ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

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

thf(2062,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) )
     != ( A @ c_Option_Ooption_ONone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(1048,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

thf(3549,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).

thf(303,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).

thf(1808,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(658,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( A @ c_Finite__Set_Olattice__class_OInf__fin @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__Inf__absorb_0) ).

thf(2659,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( A @ c_Finite__Set_Olattice__class_OInf__fin @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(1030,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(3509,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(933,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageD_0) ).

thf(3285,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).

thf(972,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ c_Option_Oset ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Option_Oset_Osimps_I2_J_0) ).

thf(3377,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ c_Option_Oset ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).

thf(605,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( B @ ( E @ ( D @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Un_0) ).

thf(2527,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( B @ ( E @ ( D @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(877,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).

thf(3153,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(664,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv2_1) ).

thf(2671,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(1544,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(387,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).

thf(2014,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(269,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).

thf(1728,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(859,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(3108,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(1025,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
      | ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).

thf(3498,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
      | ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).

thf(540,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__subset__eq_0) ).

thf(2380,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

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

thf(1971,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(297,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

thf(1793,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(184,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
       != C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).

thf(1533,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
       != C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(246,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).

thf(1671,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(217,axiom,
    ! [A: $i] :
      ( ( ( A @ c_Lattices_Olower__semilattice__class_Oinf )
        = ( A @ c_Orderings_Oord__class_Omin ) )
      | ~ ( A @ class_Lattices_Olower__semilattice )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__min_0) ).

thf(1608,plain,
    ! [A: $i] :
      ( ( ( A @ c_Lattices_Olower__semilattice__class_Oinf )
        = ( A @ c_Orderings_Oord__class_Omin ) )
      | ~ ( A @ class_Lattices_Olower__semilattice )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(832,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( B @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( D @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).

thf(3049,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( B @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( D @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(954,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

thf(3332,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).

thf(1091,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Finite__Set_Ofun__left__comm ) ) )
      | ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( F @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) )
        = ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) @ ( F @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_Ofold__rec_0) ).

thf(3649,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Finite__Set_Ofun__left__comm ) ) )
      | ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( F @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) )
        = ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) @ ( F @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).

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

thf(1867,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(78,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(1275,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

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

thf(1872,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( J @ ( D @ ( C @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( E @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( A @ hAPP ) )
        = ( E @ ( E @ ( B @ ( D @ ( C @ c_Finite__Set_Ofold ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(60,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

thf(1233,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(100,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).

thf(1327,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(1054,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Odom ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__empty_0) ).

thf(3562,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Odom ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).

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

thf(2901,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(1060,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( A @ ( A @ c_Orderings_Oord__class_Omin @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ ( A @ c_Orderings_Oord__class_Omin @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__antimono_0) ).

thf(3577,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( A @ ( A @ c_Orderings_Oord__class_Omin @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ ( A @ c_Orderings_Oord__class_Omin @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).

thf(443,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).

thf(2146,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(532,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__lower_0) ).

thf(2360,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(152,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).

thf(1458,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(295,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

thf(1788,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(139,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI2_0) ).

thf(1426,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(1039,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(3530,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).

thf(864,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(3120,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

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

thf(3429,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

thf(1756,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(92,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).

thf(1310,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(967,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(3365,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).

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

thf(2918,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( G @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ ( G @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( A @ c_Finite__Set_Ofun__left__comm ) ) )
      | ( C @ ( G @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(569,axiom,
    ! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).

thf(2448,plain,
    ! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

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

thf(2933,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Ovimage ) ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(644,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).

thf(2627,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

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

thf(2168,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(71,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).

thf(1260,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(347,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).

thf(1919,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(919,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(3253,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).

thf(377,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).

thf(1988,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(284,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

thf(1761,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(106,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(1342,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

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

thf(3481,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).

thf(969,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).

thf(3370,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(857,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( A @ ( F @ ( E @ c_Lattices_Olower__semilattice ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__assoc_0) ).

thf(3103,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( A @ ( F @ ( E @ c_Lattices_Olower__semilattice ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(292,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).

thf(1782,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(1027,axiom,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( J @ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Finite__Set_Olattice_OInf__fin ) ) )
        = ( B @ ( D @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__fin__Inf_0) ).

thf(3502,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( J @ ( I @ ( H @ ( A @ ( G @ ( F @ ( E @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Finite__Set_Olattice_OInf__fin ) ) )
        = ( B @ ( D @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).

thf(850,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(3088,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(112,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).

thf(1359,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(931,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(3281,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(872,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(3140,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(599,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int_0) ).

thf(2516,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(163,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).

thf(1482,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(334,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

thf(1887,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(473,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).

thf(2216,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(913,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(3236,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).

thf(527,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(2348,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

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

thf(3350,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) )
        = ( A @ ( C @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).

thf(1045,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

thf(3545,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).

thf(688,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice ) ) ) )
      | ( ( B @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__idem_0) ).

thf(2723,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice ) ) ) )
      | ( ( B @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(802,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(2985,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(126,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

thf(1391,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(203,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

thf(1576,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

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

thf(2173,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Map_Omap__le ) ) ) )
      | ( E @ ( D @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( F @ c_Fun_Ofun__upd ) ) ) ) @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__le ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(115,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).

thf(1366,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

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

thf(2400,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( C @ ( E @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( D @ ( B @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(182,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

thf(1529,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(368,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).

thf(1967,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(409,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).

thf(2067,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(731,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( B @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__in_0) ).

thf(2825,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( B @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(728,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( F @ ( C @ ( C @ ( E @ ( D @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__graph__insert__swap_0) ).

thf(2819,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( F @ ( C @ ( C @ ( E @ ( D @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(301,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).

thf(1803,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

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

thf(2136,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

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

thf(1904,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

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

thf(2654,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_Suc )
        = ( B @ ( A @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(906,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( B @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).

thf(3221,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( B @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(771,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( C @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__inf__iff_2) ).

thf(2916,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( C @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(928,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).

thf(3275,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).

thf(677,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( E @ ( B @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1_H_0) ).

thf(2698,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( E @ ( B @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

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

thf(2667,plain,
    tc_bool @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(523,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

thf(2339,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

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

thf(2501,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(1044,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

thf(3542,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).

thf(586,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__2 ) ) ) @ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_0) ).

thf(2488,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__2 ) ) ) @ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

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

thf(2897,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(962,axiom,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

thf(3353,plain,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).

thf(679,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).

thf(2703,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(917,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

thf(3248,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).

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

thf(3442,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).

thf(894,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(3195,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).

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

thf(3029,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ ( tc_Com_Ocom @ ( D @ ( c_Com_Obody @ hAPP ) @ c_Option_Othe ) @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ ( D @ c_Com_Ocom_OBODY @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(141,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).

thf(1430,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(1089,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__iff_1) ).

thf(3644,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).

thf(693,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).

thf(2735,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(376,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

thf(1985,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(1077,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

thf(3617,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).

thf(73,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

thf(1264,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

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

thf(1323,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(1075,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

thf(3612,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).

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

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

thf(829,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

thf(3043,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(697,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( A @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

thf(2745,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( A @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(622,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).

thf(2571,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(557,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__less__iff__gr__or__eq_0) ).

thf(2420,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(855,axiom,
    tc_bool @ class_HOL_Ominus,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).

thf(3099,plain,
    tc_bool @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(684,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ( D
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( D @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_below__fold1__iff_0) ).

thf(2713,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ( D
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( D @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).

thf(1892,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

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

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

thf(904,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).

thf(3216,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).

thf(777,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).

thf(2929,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(814,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).

thf(3014,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(447,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

thf(2158,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(288,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_0) ).

thf(1773,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

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

thf(3180,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(329,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI_0) ).

thf(1875,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(911,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

thf(3231,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).

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

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

thf(318,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ ( A @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) ) ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__Inf__fold__inf_0) ).

thf(1847,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ ( A @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) ) ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(348,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) )
     != ( A @ c_Option_Ooption_ONone ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__None__eq_1) ).

thf(1922,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) )
     != ( A @ c_Option_Ooption_ONone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(673,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(2691,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(452,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).

thf(2169,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(550,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( E @ c_Option_Ooption_ONone ) )
      | ( ( E @ ( D @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Odom ) ) )
        = ( E @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__fun__upd_1) ).

thf(2403,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( E @ c_Option_Ooption_ONone ) )
      | ( ( E @ ( D @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Odom ) ) )
        = ( E @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(1087,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( E @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I1_J_0) ).

thf(3638,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( E @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).

thf(176,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

thf(1514,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(96,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI2_0) ).

thf(1319,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(258,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).

thf(1704,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(945,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

thf(3312,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(199,axiom,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

thf(1568,plain,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

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

thf(2024,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(234,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).

thf(1641,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(508,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

thf(2301,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(306,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
       != ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).

thf(1815,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
       != ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(168,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofun__left__comm ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofun__left__comm_0) ).

thf(1494,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofun__left__comm ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(482,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ hAPP ) )
        = ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_HOL_Ominus ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).

thf(2237,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ hAPP ) )
        = ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_HOL_Ominus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(243,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).

thf(1664,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(896,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

thf(3199,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).

thf(881,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

thf(3163,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(1005,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

thf(3453,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).

thf(1038,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetprod ) ) ) )
        = ( A @ ( C @ ( E @ ( B @ c_Finite__Set_Osetprod ) ) ) @ ( D @ ( B @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__insert_0) ).

thf(3527,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetprod ) ) ) )
        = ( A @ ( C @ ( E @ ( B @ c_Finite__Set_Osetprod ) ) ) @ ( D @ ( B @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).

thf(311,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).

thf(1828,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(122,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).

thf(1383,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(611,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) )
        = ( A @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert_0) ).

thf(2540,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) )
        = ( A @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(205,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).

thf(1581,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(710,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

thf(2777,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(388,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

thf(2017,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(456,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).

thf(2178,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(476,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(2222,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(359,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).

thf(1946,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(155,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).

thf(1465,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(1037,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(3524,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).

thf(996,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( E @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I3_J_0) ).

thf(3431,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( E @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).

thf(518,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__subset_0) ).

thf(2324,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(263,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).

thf(1714,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(425,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).

thf(2105,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(844,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( E @ ( B @ c_Set_Ovimage ) ) ) @ ( D @ ( A @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__mono_0) ).

thf(3075,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( E @ ( B @ c_Set_Ovimage ) ) ) @ ( D @ ( A @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(149,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

thf(1450,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(937,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( B @ ( A @ c_Finite__Set_Olattice__class_OInf__fin @ hAPP ) )
        = ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__fin__Inf_0) ).

thf(3295,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( B @ ( A @ c_Finite__Set_Olattice__class_OInf__fin @ hAPP ) )
        = ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).

thf(712,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(2782,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

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

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

thf(579,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = E )
      | ( C = D )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(2469,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = E )
      | ( C = D )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(251,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).

thf(1682,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

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

thf(1136,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(999,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

thf(3438,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

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

thf(1864,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetprod ) ) ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetprod ) ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( E @ ( B @ c_Finite__Set_Osetprod ) ) ) @ ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetprod ) ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(433,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).

thf(2122,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

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

thf(1960,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( E @ ( B @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Omap__le ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(616,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(2555,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

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] :
      ( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( C @ ( D @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).

thf(3300,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( C @ ( D @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(81,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).

thf(1283,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(412,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).

thf(2073,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(747,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

thf(2861,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(992,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).

thf(3421,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).

thf(1028,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_Option_Ooption @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
      = ( D @ tc_Option_Ooption @ ( C @ ( F @ ( E @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__restrict_0) ).

thf(3505,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ tc_Option_Ooption @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
      = ( D @ tc_Option_Ooption @ ( C @ ( F @ ( E @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

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

thf(3361,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Map_Odom ) ) )
      = ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( D @ ( C @ ( B @ c_Map_Odom ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).

thf(952,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_4) ).

thf(3327,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).

thf(722,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

thf(2804,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(213,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).

thf(1600,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(703,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(2762,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(595,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__le_1) ).

thf(2508,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(792,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(2964,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(535,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_2) ).

thf(2367,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(1042,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( E @ ( B @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1__ring_0) ).

thf(3537,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( E @ ( B @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).

thf(351,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).

thf(1928,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(641,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Map_Orestrict__map ) ) ) )
      = ( E @ tc_Option_Ooption @ ( B @ ( C @ ( A @ hAPP ) @ ( C @ ( E @ ( B @ ( D @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__map__insert_0) ).

thf(2618,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Map_Orestrict__map ) ) ) )
      = ( E @ tc_Option_Ooption @ ( B @ ( C @ ( A @ hAPP ) @ ( C @ ( E @ ( B @ ( D @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

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

thf(2833,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = ( D @ ( A @ hAPP ) @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(499,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

thf(2281,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

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] :
      ( ~ ( E @ ( K @ ( J @ ( I @ ( A @ ( H @ ( G @ ( F @ ( C @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( E @ ( E @ ( D @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_Oinf__Inf__fold__inf_0) ).

thf(1447,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( K @ ( J @ ( I @ ( A @ ( H @ ( G @ ( F @ ( C @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( E @ ( E @ ( D @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(584,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff_0) ).

thf(2483,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(602,axiom,
    tc_bool @ class_Lattices_Obounded__lattice,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

thf(2523,plain,
    tc_bool @ class_Lattices_Obounded__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

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

thf(1796,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( K @ ( J @ ( A @ ( I @ ( H @ ( G @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( E @ ( E @ ( D @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

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

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

thf(799,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).

thf(2979,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(127,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).

thf(1394,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(708,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(2772,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) ) ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__Sup__fold__sup_0) ).

thf(1345,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) ) ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(720,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) )
        = ( C @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__Un_0) ).

thf(2799,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) )
        = ( C @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(424,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__sup_0) ).

thf(2103,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(131,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

thf(1405,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

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

thf(1943,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

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

thf(1201,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

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

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

thf(64,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).

thf(1242,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(1022,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

thf(3492,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).

thf(686,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__empty_0) ).

thf(2718,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(256,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
       != ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).

thf(1696,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
       != ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(627,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( D @ ( B @ c_Map_Omap__add ) ) ) )
        = ( C @ ( A @ ( B @ ( D @ c_Map_Omap__add ) ) ) ) )
      | ( ( C @ ( A @ ( D @ c_Map_Odom ) ) @ ( C @ ( A @ ( B @ c_Map_Odom ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__comm_0) ).

thf(2586,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ ( D @ ( B @ c_Map_Omap__add ) ) ) )
        = ( C @ ( A @ ( B @ ( D @ c_Map_Omap__add ) ) ) ) )
      | ( ( C @ ( A @ ( D @ c_Map_Odom ) ) @ ( C @ ( A @ ( B @ c_Map_Odom ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(757,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__ac_I1_J_0) ).

thf(2884,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(238,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).

thf(1651,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(215,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).

thf(1604,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

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

thf(2011,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(50,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).

thf(1206,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(1008,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(3459,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).

thf(468,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).

thf(2204,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(924,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ ( tc_Com_Ocom @ ( D @ ( c_Com_Obody @ hAPP ) @ c_Option_Othe ) @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( D @ c_Com_Ocom_OBODY @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ ( D @ c_Com_Ocom_OBODY @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BodyN_0) ).

thf(3265,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ ( tc_Com_Ocom @ ( D @ ( c_Com_Obody @ hAPP ) @ c_Option_Othe ) @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( E @ ( D @ c_Com_Ocom_OBODY @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( E @ ( D @ c_Com_Ocom_OBODY @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).

thf(948,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ononempty__iff_2) ).

thf(3318,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).

thf(480,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_Map_Odom ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( C @ ( D @ ( A @ c_Map_Odom ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ c_Option_Ooption_ONone ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__minus_0) ).

thf(2232,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_Map_Odom ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( C @ ( D @ ( A @ c_Map_Odom ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ c_Option_Ooption_ONone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(231,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(1636,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

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

thf(3418,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).

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

thf(3582,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ tc_Option_Ooption @ ( C @ ( D @ c_Option_Ooption_ONone @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
        = ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Map_Orestrict__map ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).

thf(910,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( B @ ( E @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ( D @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__le2_0) ).

thf(3229,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( B @ ( E @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ( D @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).

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

thf(3567,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = ( C @ ( D @ ( A @ ( B @ c_Map_Osko__Map__XdomD__1__1 ) ) ) @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).

thf(254,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = G )
      | ( ( F @ ( A @ hAPP ) )
        = ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
       != ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_2) ).

thf(1691,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = G )
      | ( ( F @ ( A @ hAPP ) )
        = ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
       != ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(1040,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__singleton_0) ).

thf(3531,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).

thf(47,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).

thf(1199,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(158,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__maxI1_0) ).

thf(1470,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(345,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(1915,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(260,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).

thf(1708,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(416,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).

thf(2083,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

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

thf(2496,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( G @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( D @ ( E @ c_Finite__Set_Ofinite ) )
      | ( E
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( E @ ( D @ ( F @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

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

thf(2905,plain,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(541,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

thf(2382,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(270,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).

thf(1730,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(826,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(3037,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).

thf(35,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).

thf(1163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(665,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__2 ) @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__1 ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq1_0) ).

thf(2673,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__2 ) @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__1 ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(628,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ ( B @ c_Map_Omap__le ) ) ) )
      | ( C @ ( A @ ( D @ c_Map_Odom ) ) @ ( C @ ( A @ ( B @ c_Map_Odom ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__implies__dom__le_0) ).

thf(2589,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( D @ ( B @ c_Map_Omap__le ) ) ) )
      | ( C @ ( A @ ( D @ c_Map_Odom ) ) @ ( C @ ( A @ ( B @ c_Map_Odom ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(680,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).

thf(2705,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(124,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(1387,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(634,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Option_Oset ) @ ( C @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( C @ ( B @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_elem__set_0) ).

thf(2601,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Option_Oset ) @ ( C @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( C @ ( B @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(618,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__eqI_1) ).

thf(2560,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

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

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

thf(437,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).

thf(2133,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

thf(1751,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(244,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).

thf(1666,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

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

thf(1487,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( J @ ( I @ ( C @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( E @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( A @ hAPP ) )
        = ( E @ ( E @ ( B @ ( D @ ( C @ c_Finite__Set_Ofold ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

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

thf(3610,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).

thf(794,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__graph__insert__swap_0) ).

thf(2969,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(636,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).

thf(2606,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(870,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ ( C @ ( A @ c_Set_Oinsert @ c_Finite__Set_Ofold ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_union__fold__insert_0) ).

thf(3134,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ ( C @ ( A @ c_Set_Oinsert @ c_Finite__Set_Ofold ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(918,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( D @ ( tc_bool @ ( E @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( A @ ( E @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( E @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff_0) ).

thf(3250,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( D @ ( tc_bool @ ( E @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( A @ ( E @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( E @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).

thf(1096,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv2_0) ).

thf(3664,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( A @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).

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

thf(1238,plain,
    ! [A: $i] :
      ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

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

thf(1560,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(486,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(2249,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(1071,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

thf(3603,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).

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

thf(3239,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).

thf(841,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__2 ) @ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__1 ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq2_1) ).

thf(3069,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__2 ) @ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__1 ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(309,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(1824,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(222,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).

thf(1619,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

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

thf(1370,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

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

thf(3207,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(1032,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( C @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infI_0) ).

thf(3514,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( C @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).

thf(568,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(2445,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

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

thf(2433,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( E @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = ( B @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(86,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

thf(1296,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

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

thf(1624,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(46,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

thf(1195,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

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

thf(1573,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( C @ ( B @ tc_Option_Ooption @ ( B @ c_Option_Ooption_ONone @ c_COMBK ) ) @ ( A @ c_Map_Omap__add ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(6,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

thf(1106,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

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

thf(2958,plain,
    ! [A: $i] : ( A @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(943,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(3307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(356,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

thf(1938,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(752,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_escape_0) ).

thf(2873,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(851,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( G @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 ) ) ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).

thf(3090,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( G @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 ) ) ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

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

thf(2565,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( D @ ( F @ c_Finite__Set_Ofinite ) )
      | ( F @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( G @ ( F @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__image ) ) ) ) ) )
        = ( D @ ( G @ ( F @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( E @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

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

thf(1555,plain,
    tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(946,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(3314,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).

thf(871,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(3137,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(1051,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

thf(3556,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).

thf(874,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty_0) ).

thf(3144,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(33,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(1159,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(314,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

thf(1836,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(458,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

thf(2181,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(52,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).

thf(1210,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(240,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__eq__fold__idem_0) ).

thf(1656,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(525,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).

thf(2344,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(588,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Un_0) ).

thf(2492,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

thf(1281,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

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

thf(2741,plain,
    ! [A: $i] :
      ( ( A @ c_Hoare__Mirabelle_OMGT )
      = ( tc_Com_Ostate @ ( A @ c_Natural_Oevalc @ ( A @ ( tc_Com_Ostate @ c_fequal @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

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

thf(1634,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(1097,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Map_Odom ) ) )
      = ( B @ ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__restrict_0) ).

thf(3667,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Map_Odom ) ) )
      = ( B @ ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).

thf(478,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oneq__iff_1) ).

thf(2228,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( C @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(429,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( B @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( A @ ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) ) ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__fold__sup_0) ).

thf(2112,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( B @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( A @ ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) ) ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(84,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(1291,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(274,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(1740,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(343,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__inf__le__inf_0) ).

thf(1910,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(706,axiom,
    ! [B: $i,A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).

thf(2769,plain,
    ! [B: $i,A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(1002,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( B @ ( D @ ( E @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( B @ ( C @ ( E @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__Un__disjoint_0) ).

thf(3445,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( B @ ( D @ ( E @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( B @ ( C @ ( E @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).

thf(130,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).

thf(1402,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(375,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).

thf(1983,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(430,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).

thf(2115,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(539,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).

thf(2377,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(670,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(2685,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(738,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__2 ) @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__1 ) @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq1_1) ).

thf(2841,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__2 ) @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq1__1 ) @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(674,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(2692,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(675,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

thf(2694,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(1034,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_0) ).

thf(3518,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).

thf(23,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(1138,plain,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(281,axiom,
    tc_nat @ class_Lattices_Oupper__semilattice,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

thf(1755,plain,
    tc_nat @ class_Lattices_Oupper__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

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

thf(2638,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(109,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

thf(1350,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(355,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).

thf(1936,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

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

thf(3467,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).

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

thf(1592,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( A @ ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) ) ) )
        = ( A @ ( A @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) ) ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(422,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_Orderings_Oord__class_Omax @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__lattice_0) ).

thf(2100,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_Orderings_Oord__class_Omax @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(989,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

thf(3413,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).

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

thf(1270,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(784,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

thf(2946,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(119,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).

thf(1375,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

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

thf(2973,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(16,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    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] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(58,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__diff__distrib__left_0) ).

thf(1227,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(11,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).

thf(1111,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(682,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(2709,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

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

thf(3386,plain,
    tc_bool @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).

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

thf(2726,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( B = E )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(646,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( C @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infE_1) ).

thf(2631,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( C @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(899,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).

thf(3205,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).

thf(494,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__ge_0) ).

thf(2268,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(1000,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__card__mono_0) ).

thf(3440,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).

thf(837,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

thf(3060,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(886,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).

thf(3176,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(816,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) )
        = ( A @ ( C @ c_Finite__Set_Ocard ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert__if_1) ).

thf(3018,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) )
        = ( A @ ( C @ c_Finite__Set_Ocard ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(128,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ tc_Option_Ooption @ ( F @ ( A @ ( E @ c_Option_Ooption_OSome @ hAPP ) @ ( D @ ( C @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
       != ( B @ ( E @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_1) ).

thf(1397,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( E @ tc_Option_Ooption @ ( F @ ( A @ ( E @ c_Option_Ooption_OSome @ hAPP ) @ ( D @ ( C @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
       != ( B @ ( E @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(101,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).

thf(1329,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

thf(1361,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(241,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( F @ ( E @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( ( B @ ( E @ hAPP ) )
       != ( C @ c_Option_Ooption_ONone ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__Some__iff_3) ).

thf(1659,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( F @ ( E @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( ( B @ ( E @ hAPP ) )
       != ( C @ c_Option_Ooption_ONone ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(1079,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__image ) ) ) ) ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__image__empty_0) ).

thf(3622,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__image ) ) ) ) ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).

thf(853,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_Option_Ooption_ONone @ c_Option_Oset ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__empty__eq_1) ).

thf(3094,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_Option_Ooption_ONone @ c_Option_Oset ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(415,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__sup__distrib__right_0) ).

thf(2080,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(397,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).

thf(2038,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(614,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(2551,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(661,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).

thf(2666,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(514,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(2317,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(1058,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( E @ ( D @ ( G @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( G @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__3 ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_1) ).

thf(3573,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( E @ ( D @ ( G @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( G @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__3 ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

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

thf(1419,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(575,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) )
       != ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).

thf(2460,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) )
       != ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(719,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

thf(2798,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(808,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( B @ ( E @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ( C @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__le1_0) ).

thf(3000,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( B @ ( E @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ( C @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(887,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(3179,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).

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

thf(3407,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).

thf(901,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(3210,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(733,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

thf(2830,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(42,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

thf(1182,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(750,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Odistrib__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

thf(2868,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Odistrib__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

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

thf(3596,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).

thf(1424,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(512,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(2312,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(573,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(2455,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(403,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(2053,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(483,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( A @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

thf(2240,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( A @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(316,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).

thf(1842,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(304,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).

thf(1810,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(296,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).

thf(1791,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(335,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

thf(1889,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(235,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(1644,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(219,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

thf(1612,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(654,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__insert__idem_0) ).

thf(2649,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(798,axiom,
    tc_bool @ class_Lattices_Olower__semilattice,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

thf(2978,plain,
    tc_bool @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(580,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).

thf(2472,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(915,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Map_Osko__Map__Xmap__le__def__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( B @ ( A @ c_Map_Osko__Map__Xmap__le__def__1__1 ) ) ) @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__def_2) ).

thf(3242,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Map_Osko__Map__Xmap__le__def__1__1 ) ) ) @ ( A @ hAPP ) )
       != ( D @ ( C @ ( B @ ( A @ c_Map_Osko__Map__Xmap__le__def__1__1 ) ) ) @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

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

thf(2845,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

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

thf(1266,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(245,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

thf(1668,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

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

thf(1799,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_Orderings_Oord__class_Omin @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(862,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

thf(3115,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(987,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

thf(3409,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

thf(839,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__insert_0) ).

thf(3064,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(496,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).

thf(2272,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(310,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = E )
      | ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

thf(1825,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = E )
      | ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

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

thf(2285,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(571,axiom,
    ! [B: $i,A: $i] :
      ( ( v_x @ ( B @ ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Map_Orestrict__map ) ) ) @ hAPP ) )
      = ( B @ c_Option_Ooption_ONone ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__map__to__empty_0) ).

thf(2450,plain,
    ! [B: $i,A: $i] :
      ( ( v_x @ ( B @ ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Map_Orestrict__map ) ) ) @ hAPP ) )
      = ( B @ c_Option_Ooption_ONone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(1019,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

thf(3486,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(434,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).

thf(2125,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(208,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).

thf(1588,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(1,negated_conjecture,
    ~ ( v_x @ ( v_x @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(1099,plain,
    ~ ( v_x @ ( v_x @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

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

thf(2536,plain,
    ( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
    = ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(866,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv3_0) ).

thf(3126,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( D @ c_Orderings_Olinorder ) ) )
      | ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(668,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

thf(2681,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(186,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).

thf(1539,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(736,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

thf(2836,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(151,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI1_0) ).

thf(1456,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(743,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_1) ).

thf(2851,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(484,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Finite__Set_Osetprod ) ) ) )
        = ( A @ ( B @ ( D @ ( E @ c_Finite__Set_Osetprod ) ) ) @ ( A @ ( B @ ( C @ ( E @ c_Finite__Set_Osetprod ) ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__Un__disjoint_0) ).

thf(2243,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( E @ c_Finite__Set_Osetprod ) ) ) )
        = ( A @ ( B @ ( D @ ( E @ c_Finite__Set_Osetprod ) ) ) @ ( A @ ( B @ ( C @ ( E @ c_Finite__Set_Osetprod ) ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(530,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

thf(2355,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

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

thf(1192,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( B @ hAPP ) )
        = ( D @ c_Option_Ooption_ONone ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
       != ( D @ c_Option_Ooption_ONone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

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

thf(2581,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ tc_Option_Ooption @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
        = ( D @ tc_Option_Ooption @ ( C @ ( F @ ( E @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(577,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(2465,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(594,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

thf(2505,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(978,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__le_0) ).

thf(3390,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(1043,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( D @ ( t_b @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Option_Ooption_Ooption__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit__asm_1) ).

thf(3540,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( D @ ( t_b @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Option_Ooption_Ooption__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).

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

thf(2006,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(320,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).

thf(1852,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(726,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

thf(2813,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(373,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

thf(1979,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(810,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( F @ ( C @ ( C @ ( E @ ( D @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__graph__permute__diff_0) ).

thf(3005,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( F @ ( C @ ( C @ ( E @ ( D @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(440,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).

thf(2140,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(701,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__binary_0) ).

thf(2756,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

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

thf(3083,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(897,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cut_0) ).

thf(3201,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).

thf(1759,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(226,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).

thf(1627,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(536,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(2370,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).

thf(1525,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(875,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__eq__fold_0) ).

thf(3147,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(103,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

thf(1333,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(322,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).

thf(1857,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

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

thf(3225,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).

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

thf(2546,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(885,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

thf(3173,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(197,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

thf(1563,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(337,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

thf(1895,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

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

thf(2662,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( G @ ( D @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( F @ ( E @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( F @ ( E @ ( D @ c_Com_Ocom_OSemi ) @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

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

thf(1996,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(271,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).

thf(1732,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(768,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

thf(2909,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(291,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

thf(1779,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

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

thf(3624,plain,
    ! [A: $i] : ( A @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).

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

thf(2043,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
      | ( A @ tc_Option_Ooption @ class_Finite__Set_Ofinite_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(930,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Map_Orestrict__map ) ) ) )
      = ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Map_Orestrict__map ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__restrict_0) ).

thf(3279,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Map_Orestrict__map ) ) ) )
      = ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Map_Orestrict__map ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

thf(1064,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( A @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ ( D @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__Un_0) ).

thf(3587,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( A @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( D @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ ( D @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).

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

thf(3183,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ c_Option_Othe ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(405,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).

thf(2057,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(1066,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(3592,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).

thf(262,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).

thf(1712,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(942,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty_0) ).

thf(3306,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).

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

thf(2076,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

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

thf(2748,plain,
    ! [A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( A @ c_Com_Ocom_OBODY ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(38,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).

thf(1170,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(82,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ ( E @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__atLeastAtMost_0) ).

thf(1286,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ ( E @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

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

thf(3321,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( ( A @ c_Finite__Set_Olinorder__class_OMin )
        = ( A @ ( A @ c_Orderings_Oord__class_Omin @ c_Finite__Set_Ofold1 ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__class_OMin__def__raw_0) ).

thf(1187,plain,
    ! [A: $i] :
      ( ( ( A @ c_Finite__Set_Olinorder__class_OMin )
        = ( A @ ( A @ c_Orderings_Oord__class_Omin @ c_Finite__Set_Ofold1 ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(566,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( E @ ( F @ c_Map_Odom ) ) @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( E @ ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__add ) ) ) )
        = ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( C @ ( E @ ( F @ ( A @ c_Map_Omap__add ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__upd__left_0) ).

thf(2440,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( E @ ( F @ c_Map_Odom ) ) @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( E @ ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__add ) ) ) )
        = ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( C @ ( E @ ( F @ ( A @ c_Map_Omap__add ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(552,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

thf(2408,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(892,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( C @ tc_Option_Ooption @ ( C @ c_Option_Ooption_ONone @ c_COMBK ) ) ) )
      | ( ( C @ ( B @ ( A @ c_Map_Odom ) ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__eq__empty__conv_0) ).

thf(3190,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( B @ ( C @ tc_Option_Ooption @ ( C @ c_Option_Ooption_ONone @ c_COMBK ) ) ) )
      | ( ( C @ ( B @ ( A @ c_Map_Odom ) ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(652,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

thf(2645,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(462,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( E @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( D @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( A @ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( D @ ( A @ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__image__Un__Int_0) ).

thf(2189,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( E @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( D @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( A @ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( D @ ( A @ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(806,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

thf(2995,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(558,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).

thf(2423,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(606,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(2529,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

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

thf(2235,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Set_Ocontents ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(79,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( A @ c_Finite__Set_Ofun__left__comm ) ) )
      | ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( F @ ( E @ ( D @ ( C @ ( A @ c_Finite__Set_Ofold ) ) ) ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_Ofold__fun__comm_0) ).

thf(1278,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( A @ c_Finite__Set_Ofun__left__comm ) ) )
      | ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( F @ ( E @ ( D @ ( C @ ( A @ c_Finite__Set_Ofold ) ) ) ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(382,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).

thf(2001,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(504,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).

thf(2292,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(3,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).

thf(1103,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(921,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(3257,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).

thf(1021,axiom,
    tc_bool @ class_Lattices_Oupper__semilattice,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(3491,plain,
    tc_bool @ class_Lattices_Oupper__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(923,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( F @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Orestrict__map ) ) ) )
        = ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__fun__upd_0) ).

thf(3262,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( F @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Orestrict__map ) ) ) )
        = ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).

thf(935,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(3289,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).

thf(761,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

thf(2894,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(228,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

thf(1631,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(780,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( A @ ( E @ ( D @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__iff__inf_0) ).

thf(2936,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( A @ ( E @ ( D @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(690,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).

thf(2729,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(237,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( E @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__Un_0) ).

thf(1648,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( E @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(554,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

thf(2413,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(868,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( B @ ( A @ ( F @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oless__infI2_0) ).

thf(3130,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( B @ ( A @ ( F @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(545,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).

thf(2391,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(250,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).

thf(1680,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

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

thf(2253,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(497,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ c_Suc )
        = B )
      | ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

thf(2275,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ c_Suc )
        = B )
      | ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(395,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

thf(2033,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(444,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

thf(2149,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(846,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__subset__iff_1) ).

thf(3079,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(277,axiom,
    ! [B: $i,A: $i] :
      ( ( v_x @ ( A @ ( t_a @ ( B @ ( t_a @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Orestrict__map ) ) ) @ hAPP ) )
      = ( A @ c_Option_Ooption_ONone ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__map__empty_0) ).

thf(1747,plain,
    ! [B: $i,A: $i] :
      ( ( v_x @ ( A @ ( t_a @ ( B @ ( t_a @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Orestrict__map ) ) ) @ hAPP ) )
      = ( A @ c_Option_Ooption_ONone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(190,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

thf(1548,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(350,axiom,
    tc_nat @ class_HOL_Ominus,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).

thf(1927,plain,
    tc_nat @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(393,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).

thf(2028,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(88,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(1301,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

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

thf(3375,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(211,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

thf(1595,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(603,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_0) ).

thf(2524,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(981,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_2) ).

thf(3396,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

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

thf(3343,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).

thf(879,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ( D
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( D @ ( A @ ( A @ c_Orderings_Oord__class_Omin @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__below__fold1__iff_0) ).

thf(3158,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ( D
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( D @ ( A @ ( A @ c_Orderings_Oord__class_Omin @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).

thf(491,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( B @ ( A @ ( F @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oless__infI1_0) ).

thf(2260,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( B @ ( A @ ( F @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__belowI_0) ).

thf(1154,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(977,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(3387,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).

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] :
      ( ~ ( B @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = ( D @ ( A @ hAPP ) @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).

thf(2789,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = ( D @ ( A @ hAPP ) @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(1013,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

thf(3472,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).

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

thf(2393,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(847,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageI_0) ).

thf(3081,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(927,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) )
        = ( C @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__insert_0) ).

thf(3272,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) )
        = ( C @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).

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

thf(2716,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(367,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).

thf(1965,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

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

thf(1256,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

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

thf(3599,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_The ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).

thf(790,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( E @ ( B @ c_Finite__Set_Osetprod ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( D @ ( E @ c_Finite__Set_Ofinite ) )
      | ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__zero__iff_2) ).

thf(2959,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( E @ ( B @ c_Finite__Set_Osetprod ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( D @ ( E @ c_Finite__Set_Ofinite ) )
      | ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(1046,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(3547,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).

thf(313,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(1833,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(1086,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(3636,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).

thf(912,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__greatest_0) ).

thf(3234,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).

thf(401,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).

thf(2048,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(746,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

thf(2859,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(477,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).

thf(2225,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(333,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).

thf(1884,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(220,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).

thf(1615,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(293,axiom,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

thf(1784,plain,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(125,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).

thf(1389,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(920,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__trans_0) ).

thf(3255,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).

thf(657,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

thf(2657,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(742,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

thf(2849,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

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

thf(2188,plain,
    tc_nat @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(800,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(2981,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

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

thf(3283,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).

thf(598,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( C @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__inf__iff_0) ).

thf(2514,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( C @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

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

thf(2568,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_Option_Ooption_ONone ) )
      | ( ( B @ ( A @ c_Option_Oset ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(723,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ tc_Option_Ooption @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Odom ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_Map_Odom ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__fun__upd_0) ).

thf(2806,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ tc_Option_Ooption @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Odom ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_Map_Odom ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(804,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).

thf(2991,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(257,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).

thf(1701,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

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

thf(3590,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_fequal @ hAPP ) @ c_The ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).

thf(548,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

thf(2398,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(178,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).

thf(1520,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(985,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ( ( B @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Omult__idem_0) ).

thf(3404,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ( ( B @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).

thf(24,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).

thf(1139,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(818,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_5) ).

thf(3023,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

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

thf(2220,plain,
    ( ( v_c @ c_Hoare__Mirabelle_OMGT )
    = ( tc_Com_Ostate @ ( v_c @ c_Natural_Oevalc @ ( v_c @ ( tc_Com_Ostate @ c_fequal @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(519,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).

thf(2326,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) )
       != ( D @ ( G @ ( F @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

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

thf(3051,plain,
    tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

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

thf(3077,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(694,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(2738,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(809,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( A @ c_Finite__Set_Ofun__left__comm ) ) )
      | ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( F @ ( C @ ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) )
        = ( F @ ( C @ ( E @ ( B @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_Ofold__insert2_0) ).

thf(3002,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( A @ c_Finite__Set_Ofun__left__comm ) ) )
      | ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( F @ ( C @ ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) )
        = ( F @ ( C @ ( E @ ( B @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(7,axiom,
    tc_nat @ class_Ring__and__Field_Omult__mono,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).

thf(1107,plain,
    tc_nat @ class_Ring__and__Field_Omult__mono,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(865,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).

thf(3123,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(404,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

thf(2055,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(941,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
      = ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).

thf(3304,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
      = ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).

thf(940,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).

thf(3302,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).

thf(884,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).

thf(3170,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(248,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( A @ hAPP ) )
        = ( D @ c_Option_Ooption_ONone ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
       != ( D @ c_Option_Ooption_ONone ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_1) ).

thf(1675,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( A @ hAPP ) )
        = ( D @ c_Option_Ooption_ONone ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
       != ( D @ c_Option_Ooption_ONone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(140,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

thf(1428,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(907,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Finite__Set_Ocard ) @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Diff1__less_0) ).

thf(3223,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Finite__Set_Ocard ) @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(93,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).

thf(1312,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(1090,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).

thf(3646,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).

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

thf(3340,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).

thf(1067,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(3594,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).

thf(702,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( E @ ( B @ c_Finite__Set_Osetprod ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( D @ ( E @ c_Finite__Set_Ofinite ) )
      | ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setprod__zero_0) ).

thf(2759,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( E @ ( B @ c_Finite__Set_Osetprod ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( D @ ( E @ c_Finite__Set_Ofinite ) )
      | ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(998,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_1) ).

thf(3436,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).

thf(574,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_Suc @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).

thf(2457,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_Suc @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(617,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).

thf(2557,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

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] :
      ( ~ ( B @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = ( D @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).

thf(3641,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = ( D @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).

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

thf(2425,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(990,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
      = ( B @ ( B @ ( C @ ( A @ c_Finite__Set_Ofold1Set ) ) @ c_The ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__def_0) ).

thf(3416,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
      = ( B @ ( B @ ( C @ ( A @ c_Finite__Set_Ofold1Set ) ) @ c_The ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(232,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

thf(1638,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(57,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__join ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__sup__distrib__left_0) ).

thf(1224,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__join ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(531,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

thf(2358,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(516,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__less__iff__gr__or__eq_1) ).

thf(2319,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

thf(1356,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(596,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(2510,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

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

thf(2346,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

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

thf(2521,plain,
    ! [C: $i,B: $i,A: $i] :
      ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

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

thf(2721,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

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

thf(2478,plain,
    ! [B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

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

thf(2214,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(934,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( C @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ofold1__belowI_0) ).

thf(3287,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( C @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).

thf(767,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = F )
      | ~ ( C @ ( B @ ( A @ c_Orderings_Olinorder ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_OMax__singleton_0) ).

thf(2906,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = F )
      | ~ ( C @ ( B @ ( A @ c_Orderings_Olinorder ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(353,axiom,
    tc_nat @ class_Lattices_Olattice,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

thf(1933,plain,
    tc_nat @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

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

thf(1771,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(975,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

thf(3384,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).

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

thf(1571,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(408,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).

thf(2065,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(1084,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

thf(3631,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).

thf(610,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(2538,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(132,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

thf(1408,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(651,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ ( A @ c_Orderings_Oord__class_Omin @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__strict__below__iff_2) ).

thf(2642,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ ( A @ c_Orderings_Oord__class_Omin @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(878,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).

thf(3155,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(421,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

thf(2097,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(926,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_1) ).

thf(3270,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).

thf(214,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

thf(1603,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

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

thf(2299,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

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

thf(2955,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( E @ ( B @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Finite__Set_Osetprod ) ) ) )
        = ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetprod ) ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(485,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(2246,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

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

thf(3106,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( B @ ( E @ ( D @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( E @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(187,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).

thf(1542,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(267,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

thf(1722,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(26,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    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] :
      ( ( ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(895,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).

thf(3197,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(300,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).

thf(1801,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(745,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = B )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).

thf(2856,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = B )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

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

thf(2802,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

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

thf(3500,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(465,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).

thf(2197,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(369,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).

thf(1969,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(91,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).

thf(1307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(457,axiom,
    ! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__le ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__empty_0) ).

thf(2180,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__le ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

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

thf(3219,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(330,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).

thf(1877,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(513,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( F @ ( C @ c_Finite__Set_Ofun__left__comm ) ) )
      | ~ ( B @ ( G @ ( F @ ( E @ ( D @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( G @ ( F @ ( E @ ( D @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_Ofold__graph__determ_0) ).

thf(2314,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( F @ ( C @ c_Finite__Set_Ofun__left__comm ) ) )
      | ~ ( B @ ( G @ ( F @ ( E @ ( D @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( G @ ( F @ ( E @ ( D @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).

thf(1993,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

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

thf(2780,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(660,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(2664,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(121,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).

thf(1381,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(105,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(1339,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

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

thf(2610,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(821,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( C @ c_Orderings_Olinorder ) ) )
      | ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Oantisym__conv1_1) ).

thf(3027,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ ( C @ c_Orderings_Olinorder ) ) )
      | ( B @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(835,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

thf(3055,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(195,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).

thf(1557,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(428,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

thf(2111,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(843,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).

thf(3073,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).

thf(882,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

thf(3165,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(324,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

thf(1862,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(824,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(3034,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(553,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__antimono_0) ).

thf(2410,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(99,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(1325,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

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

thf(3614,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).

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

thf(2593,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(1004,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(3451,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).

thf(28,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(1149,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

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

thf(3298,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Option_Ooption_Ooption__case ) ) ) ) )
      = ( D @ ( B @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).

thf(194,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ ( A @ c_Map_Omap__le ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__refl_0) ).

thf(1556,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( A @ ( A @ c_Map_Omap__le ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(153,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).

thf(1460,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

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

thf(2647,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(498,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( A @ ( F @ ( E @ c_Lattices_Olower__semilattice ) ) ) )
      | ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__left__commute_0) ).

thf(2278,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( A @ ( F @ ( E @ c_Lattices_Olower__semilattice ) ) ) )
      | ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(615,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( B @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__psubset_0) ).

thf(2553,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( B @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(876,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( C = B )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_OneqE_0) ).

thf(3150,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( C = B )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(362,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

thf(1952,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(769,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( A @ ( E @ ( D @ c_Lattices_Olower__semilattice ) ) ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__left__idem_0) ).

thf(2911,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( A @ ( E @ ( D @ c_Lattices_Olower__semilattice ) ) ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(307,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

thf(1820,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(12,axiom,
    tc_nat @ class_Ring__and__Field_Omult__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

thf(1112,plain,
    tc_nat @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

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

thf(2578,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ hAPP ) )
        = ( E @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(253,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( E @ ( D @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( C @ c_Option_Ooption_ONone ) )
      | ( ( B @ ( D @ hAPP ) )
       != ( C @ c_Option_Ooption_ONone ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ c_Option_Ooption_ONone ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_2) ).

thf(1688,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( E @ ( D @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( C @ c_Option_Ooption_ONone ) )
      | ( ( B @ ( D @ hAPP ) )
       != ( C @ c_Option_Ooption_ONone ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ c_Option_Ooption_ONone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) )
       != ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_1) ).

thf(1213,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) )
       != ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(642,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( D @ ( t_b @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Option_Ooption_Ooption__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit_1) ).

thf(2620,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( D @ ( t_b @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Option_Ooption_Ooption__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(40,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
     != ( E @ ( C @ tc_Option_Ooption @ ( C @ c_Option_Ooption_ONone @ c_COMBK ) ) ) ),
    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 @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
     != ( E @ ( C @ tc_Option_Ooption @ ( C @ c_Option_Ooption_ONone @ c_COMBK ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(1031,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( F @ ( E @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 ) ) ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).

thf(3512,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( F @ ( E @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 ) ) ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).

thf(960,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__leE_0) ).

thf(3348,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).

thf(469,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).

thf(2207,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(255,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).

thf(1694,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(410,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).

thf(2069,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(707,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( C @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infE_0) ).

thf(2770,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( C @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(556,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubsetD_0) ).

thf(2418,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

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

thf(2962,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_Orderings_Olinorder ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(534,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( G @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 ) ) ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_1) ).

thf(2365,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 ) ) ) @ ( F @ ( G @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( G @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 ) ) ) ) ) @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(160,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

thf(1474,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(528,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__mono_0) ).

thf(2350,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(471,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).

thf(2212,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(1082,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(3627,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).

thf(453,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ c_The ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__def_0) ).

thf(2171,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ c_The ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(704,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ tc_Option_Ooption @ ( C @ ( D @ c_Option_Ooption_ONone @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
        = ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__None__restrict_1) ).

thf(2765,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ tc_Option_Ooption @ ( C @ ( D @ c_Option_Ooption_ONone @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
        = ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(993,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ( D
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Ofold1__insert__idem_0) ).

thf(3423,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ( D
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).

thf(65,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

thf(1245,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(583,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(2481,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(860,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ c_Option_Ooption_ONone ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domIff_0) ).

thf(3110,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Map_Odom ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ c_Option_Ooption_ONone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(417,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

thf(2086,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(778,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

thf(2931,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

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] :
      ( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( D @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).

thf(2288,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( D @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(13,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

thf(1113,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

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

thf(3016,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_Com_Ocom @ ( A @ ( c_Com_Obody @ hAPP ) @ c_Option_Othe ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(289,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__trans_0) ).

thf(1775,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( B @ ( E @ c_Map_Omap__le ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).

thf(1435,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(647,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) )
        = ( C @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__Un_0) ).

thf(2633,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) )
        = ( C @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(390,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( v_x @ ( C @ ( t_a @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
      = ( C @ ( C @ tc_Option_Ooption @ ( v_x @ ( B @ hAPP ) @ ( C @ c_Option_Ooption_OSome @ ( v_x @ ( A @ hAPP ) @ c_Option_Ooption_Ooption__case ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__def_0) ).

thf(2022,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( v_x @ ( C @ ( t_a @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
      = ( C @ ( C @ tc_Option_Ooption @ ( v_x @ ( B @ hAPP ) @ ( C @ c_Option_Ooption_OSome @ ( v_x @ ( A @ hAPP ) @ c_Option_Ooption_Ooption__case ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(966,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ c_Option_Ooption_ONone @ ( C @ ( B @ c_Option_Ooption_Ooption__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osplit_0) ).

thf(3363,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( t_b @ ( t_a @ ( t_b @ c_Option_Ooption_ONone @ ( C @ ( B @ c_Option_Ooption_Ooption__case ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).

thf(161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).

thf(1477,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

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

thf(3325,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_Com_Ocom @ ( A @ ( c_Com_Obody @ hAPP ) @ c_Option_Othe ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(873,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( F @ ( E @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 ) ) ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_2) ).

thf(3142,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( F @ ( E @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 ) ) ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(793,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(2967,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(1250,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(169,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( F @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).

thf(1496,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( F @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(509,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( B @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__in_0) ).

thf(2303,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( B @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(371,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

thf(1973,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(302,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(1805,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != C )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(134,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( D @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__def_0) ).

thf(1413,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( D @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(360,axiom,
    tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

thf(1948,plain,
    tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(242,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).

thf(1662,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

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

thf(3193,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(51,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI1_0) ).

thf(1208,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(156,axiom,
    tc_nat @ class_Lattices_Odistrib__lattice,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).

thf(1467,plain,
    tc_nat @ class_Lattices_Odistrib__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

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

thf(2652,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(21,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).

thf(1134,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(489,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(2256,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(225,axiom,
    tc_nat @ class_Orderings_Obot,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

thf(1626,plain,
    tc_nat @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(1036,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

thf(3522,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).

thf(812,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__Un2_0) ).

thf(3009,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(770,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( B @ ( E @ ( D @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Int_0) ).

thf(2914,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( B @ ( E @ ( D @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(823,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(3031,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

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

thf(2816,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ hAPP ) )
        = ( D @ c_Option_Ooption_ONone ) )
      | ( D @ ( A @ ( C @ c_Map_Odom ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(206,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

thf(1583,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(36,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) ) ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__le__fold__sup_0) ).

thf(1166,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) ) ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(426,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).

thf(2107,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(515,axiom,
    ! [B: $i,A: $i] : ( A @ ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ c_Option_Oset ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_elem__set_1) ).

thf(2318,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ c_Option_Oset ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(713,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).

thf(2784,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

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

thf(3161,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(341,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

thf(1905,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(754,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(2878,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(593,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(2503,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(570,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

thf(2449,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(174,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).

thf(1509,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(776,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Onot__le_0) ).

thf(2927,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

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

thf(2629,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Finite__Set_Ocard ) @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(378,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).

thf(1990,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

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

thf(3048,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ ( c_Com_Ocom_OSKIP @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(1006,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( t_a @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__1 ) ) ) @ ( D @ hAPP ) @ c_COMBK ) ) @ ( C @ ( t_a @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__2 ) ) ) @ ( tc_bool @ ( tc_Com_Ostate @ ( tc_Com_Ostate @ ( tc_Com_Ostate @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_COMBK ) ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_escape_1) ).

thf(3455,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( t_a @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__1 ) ) ) @ ( D @ hAPP ) @ c_COMBK ) ) @ ( C @ ( t_a @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xescape__2 ) ) ) @ ( tc_bool @ ( tc_Com_Ostate @ ( tc_Com_Ostate @ ( tc_Com_Ostate @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_COMBK ) ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).

thf(159,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).

thf(1472,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(929,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

thf(3278,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).

thf(632,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( C @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__inf__iff_1) ).

thf(2597,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( D @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( C @ ( E @ ( D @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(936,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ ( A @ c_Orderings_Oord__class_Omin @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__below__iff_2) ).

thf(3292,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ ( A @ c_Orderings_Oord__class_Omin @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).

thf(763,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).

thf(2899,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(782,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_0) ).

thf(2942,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(317,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).

thf(1845,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(1029,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).

thf(3507,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).

thf(463,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).

thf(2192,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(903,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Olinear_0) ).

thf(3214,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Orderings_Olinorder ) ) )
      | ( B @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

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

thf(3129,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ hAPP ) @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(729,axiom,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( H @ ( I @ ( F @ ( G @ ( E @ ( C @ ( A @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( D @ ( I @ ( H @ ( G @ ( F @ ( tc_bool @ ( D @ ( D @ ( E @ c_COMBC ) ) ) @ ( tc_bool @ ( D @ ( D @ ( C @ c_COMBC ) ) ) @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).

thf(2821,plain,
    ! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( H @ ( I @ ( F @ ( G @ ( E @ ( C @ ( A @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( D @ ( I @ ( H @ ( G @ ( F @ ( tc_bool @ ( D @ ( D @ ( E @ c_COMBC ) ) ) @ ( tc_bool @ ( D @ ( D @ ( C @ c_COMBC ) ) ) @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(183,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Option_Ooption_Ooption__case ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I4_J_0) ).

thf(1531,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Option_Ooption_Ooption__case ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(756,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

thf(2882,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(748,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1 ) ) @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__nonempty__imp__fold1Set_0) ).

thf(2863,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xfinite__nonempty__imp__fold1Set__1__1 ) ) @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(947,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

thf(3315,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).

thf(212,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).

thf(1598,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(218,axiom,
    tc_nat @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(1611,plain,
    tc_nat @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(31,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).

thf(1156,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

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

thf(1743,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(129,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).

thf(1400,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(198,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__add ) ) ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__map__add_0) ).

thf(1566,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Map_Omap__add ) ) ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(442,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

thf(2143,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(692,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( E @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I2_J_0) ).

thf(2732,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( E @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(357,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( B @ ( B @ ( A @ c_Finite__Set_Ofun__left__comm ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofun__left__comm_0) ).

thf(1941,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( B @ ( B @ ( A @ c_Finite__Set_Ofun__left__comm ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(1009,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ c_Finite__Set_Ofinite ) )
      | ( F @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( A @ ( F @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) )
        = ( D @ ( A @ ( F @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( E @ ( B @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__image__insert_0) ).

thf(3462,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ c_Finite__Set_Ofinite ) )
      | ( F @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( A @ ( F @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) )
        = ( D @ ( A @ ( F @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( E @ ( B @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).

thf(667,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( D @ ( C @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( B @ ( B @ ( D @ ( C @ ( A @ c_Finite__Set_Ofold ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__eq__fold_0) ).

thf(2678,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( D @ ( C @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( B @ ( B @ ( D @ ( C @ ( A @ c_Finite__Set_Ofold ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(600,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) )
        = ( B @ ( A @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Diff__singleton__if_1) ).

thf(2518,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) )
        = ( B @ ( A @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(116,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).

thf(1368,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(455,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

thf(2175,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(280,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).

thf(1753,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( F @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(543,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 ) ) @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__eqI_1) ).

thf(2386,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 ) ) @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(1073,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).

thf(3608,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).

thf(1230,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(164,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

thf(1484,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Odistrib__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(448,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).

thf(2160,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(170,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).

thf(1499,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(1003,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).

thf(3448,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).

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

thf(1716,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(955,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ c_Finite__Set_Ofinite ) )
      | ( F @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( A @ ( F @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__image ) ) ) ) ) )
        = ( D @ ( A @ ( F @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( E @ ( B @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__image__insert_0) ).

thf(3334,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ c_Finite__Set_Ofinite ) )
      | ( F @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( A @ ( F @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__image ) ) ) ) ) )
        = ( D @ ( A @ ( F @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( E @ ( B @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).

thf(773,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

thf(2920,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(327,axiom,
    ! [A: $i] :
      ( ( ( A @ c_Finite__Set_Olinorder__class_OMax )
        = ( A @ ( A @ c_Orderings_Oord__class_Omax @ c_Finite__Set_Ofold1 ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__def__raw_0) ).

thf(1869,plain,
    ! [A: $i] :
      ( ( ( A @ c_Finite__Set_Olinorder__class_OMax )
        = ( A @ ( A @ c_Orderings_Oord__class_Omax @ c_Finite__Set_Ofold1 ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(294,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).

thf(1785,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(435,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

thf(2128,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(339,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).

thf(1901,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(1055,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( G @ ( F @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ( ( C @ ( C @ ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) )
        = ( C @ ( C @ ( E @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ofold__inf__insert_0) ).

thf(3564,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( G @ ( F @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ( ( C @ ( C @ ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) )
        = ( C @ ( C @ ( E @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).

thf(204,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ c_Orderings_Olinorder ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dual__linorder_0) ).

thf(1579,plain,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ c_Orderings_Olinorder ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(104,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__infinite_0) ).

thf(1336,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(142,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( E @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__Un__Int_0) ).

thf(1432,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( E @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(450,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( A @ ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) ) ) )
        = ( A @ ( A @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) ) ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__sup__insert_0) ).

thf(2165,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( A @ ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) ) ) )
        = ( A @ ( A @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) ) ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(820,axiom,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(3026,plain,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(561,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_3) ).

thf(2429,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(1093,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

thf(3655,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).

thf(72,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).

thf(1262,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(95,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).

thf(1317,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(312,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

thf(1830,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(678,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

thf(2701,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(633,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).

thf(2599,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(765,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).

thf(2903,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(964,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(3359,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).

thf(953,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
     != ( C @ c_Com_Ocom_OBODY ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).

thf(3329,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
     != ( C @ c_Com_Ocom_OBODY ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).

thf(55,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).

thf(1218,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(828,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( C @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__greatest_0) ).

thf(3041,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( C @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(666,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__int_I4_J_0) ).

thf(2675,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(285,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

thf(1766,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(737,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

thf(2838,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(278,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).

thf(1749,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(172,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).

thf(1504,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(863,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).

thf(3117,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(781,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1_1) ).

thf(2939,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(842,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_2) ).

thf(3071,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(77,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).

thf(1272,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(1035,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( G @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( F @ ( B @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Finite__Set_Ofold ) ) ) ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ofold__inf__le__inf_0) ).

thf(3520,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( G @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( F @ ( B @ hAPP ) @ hAPP ) @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Finite__Set_Ofold ) ) ) ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).

thf(811,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(3007,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(354,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).

thf(1934,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

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

thf(2948,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2 ) @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1 ) @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__2 ) @ ( A @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__Xfold1__in__1__1 ) @ ( B @ hAPP ) @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( C @ ( A @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(338,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).

thf(1898,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( E @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(1092,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).

thf(3652,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).

thf(70,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
        = A )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__triv_0) ).

thf(1257,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
        = A )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(25,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).

thf(1141,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(185,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

thf(1536,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(374,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

thf(1981,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(612,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__left__commute_0) ).

thf(2543,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(963,axiom,
    ! [A: $i] :
      ( ( A @ c_Com_Ocom_OBODY )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).

thf(3356,plain,
    ! [A: $i] :
      ( ( A @ c_Com_Ocom_OBODY )
     != c_Com_Ocom_OSKIP ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).

thf(56,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).

thf(1221,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(797,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ hAPP ) )
        = ( D @ c_Option_Ooption_ONone ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__out_0) ).

thf(2975,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ hAPP ) )
        = ( D @ c_Option_Ooption_ONone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(110,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

thf(1353,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( C @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(363,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

thf(1955,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(739,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_0) ).

thf(2843,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(683,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(2711,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(173,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).

thf(1506,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).

thf(1372,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

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

thf(2892,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( G @ ( F @ ( C @ ( E @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ( G @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(626,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(2584,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(982,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Nitpick_Ofold__graph_H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).

thf(3398,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Nitpick_Ofold__graph_H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).

thf(63,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).

thf(1240,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(221,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).

thf(1617,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(753,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ hAPP ) )
        = C )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
       != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).

thf(2875,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ hAPP ) )
        = C )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(1007,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_0) ).

thf(3457,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).

thf(840,axiom,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(3067,plain,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).

thf(252,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

thf(1685,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(177,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

thf(1517,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

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

thf(1216,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_Orderings_Oord__class_Omax @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(202,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

thf(1575,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(381,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).

thf(1998,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(137,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( F @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__find__right_0) ).

thf(1421,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( F @ ( A @ ( E @ c_Map_Omap__add ) ) ) @ hAPP ) )
        = ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(775,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( A @ ( E @ ( D @ c_Lattices_Olower__semilattice ) ) ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__commute_0) ).

thf(2924,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( A @ ( E @ ( D @ c_Lattices_Olower__semilattice ) ) ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

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

thf(1839,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Option_Ooption_ONone )
     != ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

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

thf(3620,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).

thf(984,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

thf(3401,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).

thf(418,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( C @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).

thf(2088,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( C @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(400,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( A @ hAPP ) )
        = ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
       != ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_0) ).

thf(2045,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( A @ hAPP ) )
        = ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( ( F @ ( C @ tc_Option_Ooption @ ( E @ ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
       != ( G @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(852,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_0) ).

thf(3092,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(676,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( C @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).

thf(2696,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( C @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(192,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).

thf(1553,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(361,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

thf(1949,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(751,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

thf(2870,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(732,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).

thf(2828,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(414,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

thf(2078,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(97,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).

thf(1321,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(891,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( B @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infI1_0) ).

thf(3188,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( B @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).

thf(1047,axiom,
    tc_bool @ class_Finite__Set_Ofinite_Ofinite,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).

thf(3548,plain,
    tc_bool @ class_Finite__Set_Ofinite_Ofinite,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).

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

thf(2194,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) )
        = ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(1081,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_Suc @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

thf(3625,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_Suc @ ( B @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).

thf(18,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).

thf(1126,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

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

thf(2743,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

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

thf(2997,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ c_Finite__Set_Ofun__left__comm ) ) )
      | ~ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) )
        = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(587,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(2490,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(83,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).

thf(1289,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(150,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( B @ ( B @ ( D @ ( C @ ( A @ c_Finite__Set_Ofold ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Ofold1__eq__fold__idem_0) ).

thf(1453,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( B @ ( B @ ( D @ ( C @ ( A @ c_Finite__Set_Ofold ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(411,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).

thf(2071,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(709,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__3 ) ) ) @ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_2) ).

thf(2775,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( F @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__3 ) ) ) @ ( F @ ( D @ ( E @ ( B @ v_sko__Hoare__Mirabelle__Xconseq12__1 ) ) ) @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(272,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) )
        = ( B @ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( B @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__Un__disjoint_0) ).

thf(1734,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) )
        = ( B @ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( B @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( E @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(717,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).

thf(2792,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(8,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

thf(1108,plain,
    tc_nat @ class_Ring__and__Field_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(827,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_2) ).

thf(3039,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(1018,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(3484,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(233,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).

thf(1639,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(551,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Ominus )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).

thf(2406,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Ominus )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

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

thf(2532,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(730,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( D @ ( C @ ( B @ ( A @ c_Map_Osko__Map__Xmap__le__def__1__1 ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__def_1) ).

thf(2823,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Map_Odom ) ) @ ( D @ ( C @ ( B @ ( A @ c_Map_Osko__Map__Xmap__le__def__1__1 ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(276,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).

thf(1745,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(795,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).

thf(2971,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

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

thf(1822,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(1033,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

thf(3516,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).

thf(968,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).

thf(3368,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).

thf(849,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( D
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Ofold1__Un2_0) ).

thf(3085,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( D
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(1010,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

thf(3465,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).

thf(629,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

thf(2591,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(209,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).

thf(1590,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(236,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

thf(1646,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(567,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UnI_0) ).

thf(2443,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(68,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

thf(1253,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(681,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).

thf(2707,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(803,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__Un_0) ).

thf(2988,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).

thf(1385,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(266,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

thf(1721,plain,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(500,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_1) ).

thf(2283,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(544,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).

thf(2389,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(744,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
     != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(2853,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
     != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

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

thf(2290,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Obounded__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(487,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(2251,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(725,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(2811,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(227,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).

thf(1629,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

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

thf(2004,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(392,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

thf(2026,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(1083,axiom,
    tc_bool @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(3630,plain,
    tc_bool @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).

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

thf(2608,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(562,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( B @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infI2_0) ).

thf(2431,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( B @ ( F @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(604,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).

thf(2526,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(555,axiom,
    ! [B: $i,A: $i] :
      ( ( v_x @ ( B @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__Int__eq_0) ).

thf(2416,plain,
    ! [B: $i,A: $i] :
      ( ( v_x @ ( B @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(445,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ tc_Option_Ooption @ ( G @ ( F @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( E @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( B = E )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_4) ).

thf(2152,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ tc_Option_Ooption @ ( G @ ( F @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( E @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( B = E )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(492,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

thf(2262,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(783,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__subset__iff_0) ).

thf(2944,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(167,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).

thf(1491,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).

thf(1440,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(623,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(2576,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(259,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).

thf(1706,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(533,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).

thf(2362,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(459,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

thf(2183,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(432,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).

thf(2120,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(1049,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(3552,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).

thf(389,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

thf(2019,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(34,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).

thf(1161,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(542,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).

thf(2384,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(581,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( A @ c_Map_Odom ) ) @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
        = ( C @ ( E @ ( A @ c_Map_Odom ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__dom_0) ).

thf(2475,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( E @ ( A @ c_Map_Odom ) ) @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
        = ( C @ ( E @ ( A @ c_Map_Odom ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( D @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

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

thf(2786,plain,
    tc_bool @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(1063,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(3585,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).

thf(290,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).

thf(1777,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(925,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__eqI_0) ).

thf(3267,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).

thf(85,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).

thf(1294,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(479,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_1) ).

thf(2230,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(505,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).

thf(2294,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(396,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).

thf(2036,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(589,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__2 ) @ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__1 ) @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq2_0) ).

thf(2494,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( E @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__2 ) @ ( E @ ( D @ v_sko__Hoare__Mirabelle__Xconseq2__1 ) @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

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

thf(1444,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( C @ ( B @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_COMBK ) ) @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(146,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).

thf(1442,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(423,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

thf(2102,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(175,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__inf_0) ).

thf(1512,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(669,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(2683,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

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

thf(1725,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__le ) ) ) )
      | ~ ( D @ ( C @ ( A @ ( B @ c_Map_Omap__le ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(364,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

thf(1957,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(249,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).

thf(1678,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(801,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(2983,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(1070,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_6) ).

thf(3601,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).

thf(189,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(1546,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(856,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) )
        = ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) @ c_Suc ) )
      | ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Suc__eq_5) ).

thf(3100,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) )
        = ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) @ c_Suc ) )
      | ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(786,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

thf(2951,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(1024,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).

thf(3496,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).

thf(1012,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__empty_0) ).

thf(3469,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_OSup__class_OSup ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).

thf(441,axiom,
    tc_nat @ class_Lattices_Olower__semilattice,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).

thf(2142,plain,
    tc_nat @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(973,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

thf(3379,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( ( A @ c_Finite__Set_Olattice__class_OInf__fin )
        = ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__fin__def__raw_0) ).

thf(1116,plain,
    ! [A: $i] :
      ( ( ( A @ c_Finite__Set_Olattice__class_OInf__fin )
        = ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

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

thf(1908,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
      = ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(1094,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).

thf(3658,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).

thf(474,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).

thf(2218,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

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

thf(2258,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_The ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(538,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( D
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( D @ ( C @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__insert_0) ).

thf(2374,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( D
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( D @ ( C @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(108,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).

thf(1348,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(446,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(2155,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(608,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).

thf(2534,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

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

thf(3373,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(635,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).

thf(2604,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(385,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

thf(2008,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(89,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).

thf(1303,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

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

thf(1527,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(956,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(3337,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).

thf(247,axiom,
    ! [A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).

thf(1673,plain,
    ! [A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(869,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(3132,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(66,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).

thf(1248,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(402,axiom,
    ! [A: $i] :
      ( ( ( A @ c_Lattices_Oupper__semilattice__class_Osup )
        = ( A @ c_Orderings_Oord__class_Omax ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__max_0) ).

thf(2050,plain,
    ! [A: $i] :
      ( ( ( A @ c_Lattices_Oupper__semilattice__class_Osup )
        = ( A @ c_Orderings_Oord__class_Omax ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(705,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(2768,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

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

thf(1480,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

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

thf(3203,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( D @ c_Orderings_Olinorder ) ) )
      | ~ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

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

thf(3062,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(323,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
       != B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).

thf(1859,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
       != B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(699,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( F @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Orestrict__map ) ) ) )
        = ( E @ ( D @ ( F @ ( A @ c_Map_Orestrict__map ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__fun__upd_1) ).

thf(2751,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( D @ ( F @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Orestrict__map ) ) ) )
        = ( E @ ( D @ ( F @ ( A @ c_Map_Orestrict__map ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(467,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__inf__sup_0) ).

thf(2201,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(460,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(2186,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(1052,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).

thf(3558,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).

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

thf(1710,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(994,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( A @ c_Finite__Set_Ofun__left__comm ) ) )
      | ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_Ofun__left__comm_0) ).

thf(3426,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( A @ c_Finite__Set_Ofun__left__comm ) ) )
      | ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).

thf(398,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).

thf(2040,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != ( F @ ( C @ ( E @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(663,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__commute_0) ).

thf(2668,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(830,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__Un_0) ).

thf(3045,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

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

thf(3309,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( A @ c_Finite__Set_Ofun__left__comm ) ) )
      | ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ( ( F @ ( C @ ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) )
        = ( F @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(648,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ tc_Option_Ooption @ ( B @ ( D @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Odom ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__eq__singleton__conv_1) ).

thf(2636,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ tc_Option_Ooption @ ( B @ ( D @ ( A @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ ( A @ tc_Option_Ooption @ ( A @ c_Option_Ooption_ONone @ c_COMBK ) ) @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Odom ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(1363,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

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

thf(1314,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(521,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_Orderings_Olinorder ) ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ ( C @ c_COMBC ) ) ) @ ( tc_bool @ ( B @ ( B @ ( A @ c_COMBC ) ) ) @ c_Orderings_Olinorder ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder_Odual__linorder_0) ).

thf(2334,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_Orderings_Olinorder ) ) )
      | ( B @ ( tc_bool @ ( B @ ( B @ ( C @ c_COMBC ) ) ) @ ( tc_bool @ ( B @ ( B @ ( A @ c_COMBC ) ) ) @ c_Orderings_Olinorder ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(1053,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).

thf(3560,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).

thf(1016,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Com_Ostate @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Hoare__Mirabelle_OMGT @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( tc_Com_Ostate @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Com_Ostate @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
      | ( tc_Com_Ostate @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Com_Ostate @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGF__complete_0) ).

thf(3479,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_Com_Ostate @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Hoare__Mirabelle_OMGT @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( tc_Com_Ostate @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Com_Ostate @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
      | ( tc_Com_Ostate @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_Com_Ostate @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

thf(1410,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(419,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).

thf(2091,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(950,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).

thf(3323,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).

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

thf(2795,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
        = B )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(1085,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__eq__fold_0) ).

thf(3633,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).

thf(1236,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(691,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(2731,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(19,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    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] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

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

thf(3025,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(29,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
      | ( C @ ( D @ ( C @ tc_Option_Ooption @ ( D @ ( F @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( C @ tc_Option_Ooption @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__le ) ) ) ) ),
    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 @ ( D @ ( E @ ( A @ c_Map_Omap__le ) ) ) )
      | ( C @ ( D @ ( C @ tc_Option_Ooption @ ( D @ ( F @ ( C @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ ( E @ c_Fun_Ofun__upd ) ) ) ) @ ( C @ tc_Option_Ooption @ ( D @ ( C @ c_Option_Ooption_ONone @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Omap__le ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(120,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

thf(1378,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( C @ ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

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] :
      ( ~ ( B @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = ( D @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).

thf(2265,plain,
    ! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ hAPP ) )
        = ( D @ ( C @ ( E @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(578,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).

thf(2467,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(922,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( A @ c_Finite__Set_Ofun__left__comm ) ) )
      | ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( F @ ( C @ ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) )
        = ( F @ ( C @ ( E @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm_Ofold__insert_0) ).

thf(3259,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( A @ c_Finite__Set_Ofun__left__comm ) ) )
      | ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( F @ ( C @ ( E @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) )
        = ( F @ ( C @ ( E @ ( B @ ( A @ c_Finite__Set_Ofold ) ) ) ) @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).

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

thf(3489,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(916,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) )
       != ( C @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).

thf(3245,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) )
       != ( C @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(979,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_0) ).

thf(3392,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(349,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dual__semilattice_0) ).

thf(1925,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(87,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).

thf(1299,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(1023,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__iff_2) ).

thf(3494,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).

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

thf(2372,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(439,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(2138,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) )
       != ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).

thf(1930,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) )
       != ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

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

thf(2353,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
      = ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(836,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).

thf(3057,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(741,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( F @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( G @ ( F @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).

thf(2847,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( F @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( G @ ( F @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(1057,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
        = ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).

thf(3570,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
        = ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).

thf(1072,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

thf(3605,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).

thf(988,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(3411,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).

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

thf(2485,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(372,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Option_Ooption_ONone )
     != ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).

thf(1976,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Option_Ooption_ONone )
     != ( B @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(191,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).

thf(1550,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(671,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).

thf(2687,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(331,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( F @ ( D @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
      = ( D @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( D @ ( F @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__upd_0) ).

thf(1880,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( F @ ( D @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( B @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ c_Map_Omap__add ) ) ) )
      = ( D @ tc_Option_Ooption @ ( F @ ( E @ ( D @ c_Option_Ooption_OSome @ hAPP ) @ ( C @ ( D @ ( F @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(861,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( B @ ( A @ ( D @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).

thf(3113,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( B @ ( A @ ( D @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(980,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(3394,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).

thf(495,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).

thf(2270,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(223,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

thf(1621,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(700,axiom,
    ! [B: $i,A: $i] :
      ( ( v_x @ ( B @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__Un__eq_0) ).

thf(2754,plain,
    ! [B: $i,A: $i] :
      ( ( v_x @ ( B @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( A @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( t_a @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(650,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(2640,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(1061,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

thf(3580,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).

thf(366,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

thf(1962,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

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

thf(3212,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(758,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph__insert__swap_0) ).

thf(2887,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ ( A @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( A @ ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(564,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(2436,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(406,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(2059,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

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

thf(1416,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

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

thf(3052,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( J @ ( I @ ( A @ ( H @ ( G @ ( F @ ( D @ ( E @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
      | ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Finite__Set_Olattice_OSup__fin ) ) )
        = ( B @ ( D @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

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

thf(3553,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C = D )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( D @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).

thf(157,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).

thf(1468,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(1098,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( A @ ( E @ ( D @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__absorb2_0) ).

thf(3669,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( A @ ( E @ ( D @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).

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

thf(1331,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(216,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).

thf(1606,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ c_HOL_Ozero__class_Ozero @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

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

thf(3474,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(517,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( E @ ( B @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1_0) ).

thf(2321,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( E @ ( B @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(239,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( B @ hAPP ) )
        = ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( ( E @ ( B @ hAPP ) )
        = ( D @ c_Option_Ooption_ONone ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
       != ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__SomeD_0) ).

thf(1653,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( B @ hAPP ) )
        = ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( ( E @ ( B @ hAPP ) )
        = ( D @ c_Option_Ooption_ONone ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
       != ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(909,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ ( E @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(3227,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ ( E @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(619,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_0) ).

thf(2563,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 ) ) ) @ ( C @ ( D @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 ) ) ) @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
      | ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(755,axiom,
    tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Obody @ c_Map_Odom ) ) @ c_Finite__Set_Ofinite ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__dom__body_0) ).

thf(2881,plain,
    tc_Com_Opname @ ( tc_Com_Ocom @ ( tc_Com_Opname @ ( c_Com_Obody @ c_Map_Odom ) ) @ c_Finite__Set_Ofinite ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(854,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( A @ ( E @ ( D @ c_Lattices_Olower__semilattice ) ) ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
       != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__iff__inf_1) ).

thf(3096,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( A @ ( E @ ( D @ c_Lattices_Olower__semilattice ) ) ) )
      | ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

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

thf(1737,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

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

thf(2690,plain,
    tc_bool @ class_Lattices_Odistrib__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

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

thf(1463,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(749,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).

thf(2866,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(734,axiom,
    tc_bool @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(2832,plain,
    tc_bool @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(565,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(2438,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

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

thf(1490,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Map_Omap__add ) ) ) @ ( A @ c_Map_Omap__le ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(506,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

thf(2297,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(640,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) )
        = ( C @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__insert_0) ).

thf(2615,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) )
        = ( C @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(286,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).

thf(1769,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(346,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

thf(1917,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

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

thf(2993,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(49,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).

thf(1204,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(305,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

thf(1812,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(344,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( B @ hAPP ) )
        = ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( ( E @ ( A @ hAPP ) )
        = ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
       != ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__SomeD_1) ).

thf(1912,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( B @ hAPP ) )
        = ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( ( E @ ( A @ hAPP ) )
        = ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Omap__add ) ) ) @ hAPP ) )
       != ( F @ ( D @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(825,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(3035,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

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

thf(3575,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( B @ ( D @ ( C @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Ofold1Set ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(3720,plain,
    $false,
    inference(e,[status(thm)],[2163,1718,2094,2612,1633,3661,3399,1105,2463,2427,1110,2199,3021,1586,1501,2452,2889,1190,1168,2306,3345,2341,2336,2109,2131,2031,3434,3167,2921,3477,2787,2595,1850,2499,1179,2331,3185,2210,2117,1882,2622,2953,3012,1269,1305,1437,3382,1173,1855,3534,1158,2309,2512,2808,1522,2395,2062,3549,1808,2659,3509,3285,3377,2527,3153,2671,1544,2014,1728,3108,3498,2380,1971,1793,1533,1671,1608,3049,3332,3649,1867,1275,1872,1233,1327,3562,2901,3577,2146,2360,1458,1788,1426,3530,3120,3429,1756,1310,3365,2918,2448,2933,2627,2168,1260,1919,3253,1988,1761,1342,3481,3370,3103,1782,3502,3088,1359,3281,3140,2516,1482,1887,2216,3236,2348,3350,3545,2723,2985,1391,1576,2173,1366,2400,1529,1967,2067,2825,2819,1803,2136,1904,2654,3221,2916,3275,2698,2667,2339,2501,3542,2488,2897,3353,2703,3248,3442,3195,3029,1430,3644,2735,1985,3617,1264,1323,3612,1132,3043,2745,2571,2420,3099,2713,1892,1147,3216,2929,3014,2158,1773,3180,1875,3231,1100,1847,1922,2691,2169,2403,3638,1514,1319,1704,3312,1568,2024,1641,2301,1815,1494,2237,1664,3199,3163,3453,3527,1828,1383,2540,1581,2777,2017,2178,2222,1946,1465,3524,3431,2324,1714,2105,3075,1450,3295,2782,1109,2469,1682,1136,3438,1864,2122,1960,2555,3300,1283,2073,2861,3421,3505,3361,3327,2804,1600,2762,2508,2964,2367,3537,1928,2618,2833,2281,1447,2483,2523,1796,1119,2979,1394,2772,1345,2799,2103,1405,1943,1201,1104,1242,3492,2718,1696,2586,2884,1651,1604,2011,1206,3459,2204,3265,3318,2232,1636,3418,3582,3229,3567,1691,3531,1199,1470,1915,1708,2083,2496,2905,2382,1730,3037,1163,2673,2589,2705,1387,2601,2560,1123,2133,1751,1666,1487,3610,2969,2606,3134,3250,3664,1238,1560,2249,3603,3239,3069,1824,1619,1370,3207,3514,2445,2433,1296,1624,1195,1573,1106,2958,3307,1938,2873,3090,2565,1555,3314,3137,3556,3144,1159,1836,2181,1210,1656,2344,2492,1281,2741,1634,3667,2228,2112,1291,1740,1910,2769,3445,1402,1983,2115,2377,2685,2841,2692,2694,3518,1138,1755,2638,1350,1936,3467,1592,2100,3413,1270,2946,1375,2973,1121,1227,1111,2709,3386,2726,2631,3205,2268,3440,3060,3176,3018,1397,1329,1361,1659,3622,3094,2080,2038,2551,2666,2317,3573,1419,2460,2798,3000,3179,3407,3210,2830,1182,2868,3596,1424,2312,2455,2053,2240,1842,1810,1791,1889,1644,1612,2649,2978,2472,3242,2845,1266,1668,1799,3115,3409,3064,2272,1825,2285,2450,3486,2125,1588,1099,2536,3126,2681,1539,2836,1456,2851,2243,2355,1192,2581,2465,2505,3390,3540,2006,1852,2813,1979,3005,2140,2756,3083,3201,1759,1627,2370,1525,3147,1333,1857,3225,2546,3173,1563,1895,2662,1996,1732,2909,1779,3624,2043,3279,3587,3183,2057,3592,1712,3306,2076,2748,1170,1286,3321,1187,2440,2408,3190,2645,2189,2995,2423,2529,2235,1278,2001,2292,1103,3257,3491,3262,3289,2894,1631,2936,2729,1648,2413,3130,2391,1680,2253,2275,2033,2149,3079,1747,1548,1927,2028,1301,3375,1595,2524,3396,3343,3158,2260,1154,3387,2789,3472,2393,3081,3272,2716,1965,1256,3599,2959,3547,1833,3636,3234,2048,2859,2225,1884,1615,1784,1389,3255,2657,2849,2188,2981,3283,2514,2568,2806,2991,1701,3590,2398,1520,3404,1139,3023,2220,2326,3051,3077,2738,3002,1107,3123,2055,3304,3302,3170,1675,1428,3223,1312,3646,3340,3594,2759,3436,2457,2557,3641,2425,3416,1638,1224,2358,2319,1356,2510,2346,2521,2721,2478,2214,3287,2906,1933,1771,3384,1571,2065,3631,2538,1408,2642,3155,2097,3270,1603,2299,2955,2246,3106,1542,1722,1144,3197,1801,2856,2802,3500,2197,1969,1307,2180,3219,1877,2314,1993,2780,2664,1381,1339,2610,3027,3055,1557,2111,3073,3165,1862,3034,2410,1325,3614,2593,3451,1149,3298,1556,1460,2647,2278,2553,3150,1952,2911,1820,1112,2578,1688,1213,2620,1176,3512,3348,2207,1694,2069,2770,2418,2962,2365,1474,2350,2212,3627,2171,2765,3423,1245,2481,3110,2086,2931,2288,1113,3016,1775,1435,2633,2022,3363,1477,3325,3142,2967,1250,1496,2303,1973,1805,1413,1948,1662,3193,1208,1467,2652,1134,2256,1626,3522,3009,2914,3031,2816,1583,1166,2107,2318,2784,3161,1905,2878,2503,2449,1509,2927,2629,1990,3048,3455,1472,3278,2597,3292,2899,2942,1845,3507,2192,3214,3129,2821,1531,2882,2863,3315,1598,1611,1156,1743,1400,1566,2143,2732,1941,3462,2678,2518,1368,2175,1753,2386,3608,1230,1484,2160,1499,3448,1716,3334,2920,1869,1785,2128,1901,3564,1579,1336,1432,2165,3026,2429,3655,1262,1317,1830,2701,2599,2903,3359,3329,1218,3041,2675,1766,2838,1749,1504,3117,2939,3071,1272,3520,3007,1934,2948,1898,3652,1257,1141,1536,1981,2543,3356,1221,2975,1353,1955,2843,2711,1506,1372,2892,2584,3398,1240,1617,2875,3457,3067,1685,1517,1216,1575,1998,1421,2924,1839,3620,3401,2088,2045,3092,2696,1553,1949,2870,2828,2078,1321,3188,3548,2194,3625,1126,2743,2997,2490,1289,1453,2071,2775,1734,2792,1108,3039,3484,1639,2406,2532,2823,1745,2971,1822,3516,3368,3085,3465,2591,1590,1646,2443,1253,2707,2988,1385,1721,2283,2389,2853,2290,2251,2811,1629,2004,2026,3630,2608,2431,2526,2416,2152,2262,2944,1491,1440,2576,1706,2362,2183,2120,3552,2019,1161,2384,2475,2786,3585,1777,3267,1294,2230,2294,2036,2494,1444,1442,2102,1512,2683,1725,1957,1678,2983,3601,1546,3100,2951,3496,3469,2142,3379,1116,1908,3658,2218,2258,2374,1348,2155,2534,3373,2604,2008,1303,1527,3337,1673,3132,1248,2050,2768,1480,3203,3062,1859,2751,2201,2186,3558,1710,3426,2040,2668,3045,3309,2636,1363,1314,2334,3560,3479,1410,2091,3323,2795,3633,1236,2731,1129,3025,1152,1378,2265,2467,3259,3489,3245,3392,1925,1299,3494,2372,2138,1930,2353,3057,2847,3570,3605,3411,2485,1976,1550,2687,1880,3113,3394,2270,1621,2754,2640,3580,1962,3212,2887,2436,2059,1416,3052,3553,1468,3669,1331,1606,3474,2321,1653,3227,2563,2881,3096,1737,2690,1463,2866,2832,2438,1490,2297,2615,1769,1917,2993,1204,1812,1912,3035,3575]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV875-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40  % Computer : n002.cluster.edu
% 0.14/0.40  % Model    : x86_64 x86_64
% 0.14/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40  % Memory   : 8046.5625MB
% 0.14/0.40  % OS       : Linux 6.8.0-71-generic
% 0.14/0.40  % CPULimit : 300
% 0.14/0.40  % WCLimit  : 300
% 0.14/0.40  % DateTime : Sat Sep 26 15:08:35 UTC 2026
% 0.14/0.41  % CPUTime  : 
% 0.14/0.41  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.91/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.81/1.50  % [INFO] 	 Parsing done (509ms). 
% 2.81/1.52  % [INFO] 	 Running in sequential loop mode. 
% 3.31/1.89  % [INFO] 	 eprover registered as external prover. 
% 3.49/1.90  % [INFO] 	 Scanning for conjecture ... 
% 4.60/2.21  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1106 axioms. Running axiom selection ... 
% 6.43/2.63  % [INFO] 	 Axiom selection finished. Selected 1096 axioms (removed 10 axioms). 
% 8.00/3.13  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 8.41/3.17  % [INFO] 	 Type checking passed. 
% 8.41/3.17  % [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 ... 
% 26.92/7.57  % External prover 'e' found a proof!
% 26.92/7.57  % [INFO] 	 Killing All external provers ... 
% 26.92/7.57  % Time passed: 7017ms (effective reasoning time: 6048ms)
% 26.92/7.58  % 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, cls_Diff__Un_0, cls_setsum__Un__disjoint_0, cls_ab__semigroup__mult_Omult__ac_I1_J_0, cls_Inf__lower_0, cls_insert__absorb_0, cls_evalc_OSemi_0, cls_ab__semigroup__idem__mult__inf_0, cls_empty__iff_0, cls_Min__le_0, cls_complete__lattice_OInf__fold__inf_0, cls_class__semiring_Osemiring__rules_I10_J_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_sup__le__fold__sup_0, cls_setsum__Un__Int_0, cls_Suc__lessI_0, cls_Int__subset__iff_2, cls_less__Suc__eq_2, cls_atLeastatMost__psubset__iff_3, cls_le__inf__iff_1, cls_fold__graph__imp__finite_0, clsarity_bool__HOL_Ominus, cls_not__less__eq_1, cls_Diff__subset__conv_0, cls_less__supI1_0, cls_min__less__iff__disj_0, cls_Int__Un__distrib2_0, cls_restrict__map__insert_0, cls_mult__nonpos__nonneg_0, cls_map__le__iff__map__add__commute_0, cls_mem__def_1, cls_inf1E_1, cls_Diff__triv_0, cls_complete__lattice_OSup__fold__sup_0, cls_comm__monoid__add_Omult__assoc_0, cls_sup__inf__distrib2_0, cls_fun__upd__None__restrict_0, cls_le__sup__iff_0, 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% 26.92/7.58  % No. of inferences in proof: 2197
% 26.92/7.59  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7017 ms resp. 6048 ms w/o parsing
% 30.00/8.32  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.00/8.33  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------