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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV844-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n007.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 09:00:46 AM UTC 2026

% Result   : Unsatisfiable 25.38s 10.05s
% Output   : Refutation 27.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      : 1042
% Syntax   : Number of formulae    : 2085 ( 401 unt;   0 typ;   0 def)
%            Number of atoms       : 5123 (1242 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 44146 (2784   ~;3038   |;   0   &;38324   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  130 ( 128 usr;  18 con; 0-6 aty)
%            Number of variables   : 7206 (   0   ^;7206   !;   0   ?;7206   :)

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

thf(v_F_decl,type,
    v_F: $i ).

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

thf(hBOOL_decl,type,
    hBOOL: $i > $o ).

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

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

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

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

thf(v_P_H_decl,type,
    v_P_H: $i ).

thf(v_c0_decl,type,
    v_c0: $i ).

thf(v_Q_H_decl,type,
    v_Q_H: $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_Hoare__Mirabelle_Otriple_decl,type,
    tc_Hoare__Mirabelle_Otriple: $i > $i ).

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

thf(c_Set_Oimage_decl,type,
    c_Set_Oimage: $i > $i > $i > $i > $i ).

thf(c_COMBS_decl,type,
    c_COMBS: $i > $i > $i > $i > $i > $i ).

thf(c_COMBB_decl,type,
    c_COMBB: $i > $i > $i > $i > $i > $i ).

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

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

thf(v_P_decl,type,
    v_P: $i ).

thf(v_Q_decl,type,
    v_Q: $i ).

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

thf(class_Ring__and__Field_Oidom_decl,type,
    class_Ring__and__Field_Oidom: $i > $o ).

thf(class_Int_Onumber__ring_decl,type,
    class_Int_Onumber__ring: $i > $o ).

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

thf(c_HOL_Ouminus__class_Ouminus_decl,type,
    c_HOL_Ouminus__class_Ouminus: $i > $i ).

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

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

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

thf(c_Orderings_Otop__class_Otop_decl,type,
    c_Orderings_Otop__class_Otop: $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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(c_SetInterval_Oord__class_OatLeastLessThan_decl,type,
    c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).

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

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

thf(c_SetInterval_Oord__class_OgreaterThanAtMost_decl,type,
    c_SetInterval_Oord__class_OgreaterThanAtMost: $i > $i > $i > $i ).

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

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

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

thf(class_Lattices_Oboolean__algebra_decl,type,
    class_Lattices_Oboolean__algebra: $i > $o ).

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

thf(c_Fun_Oinj__on_decl,type,
    c_Fun_Oinj__on: $i > $i > $i > $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(class_Ring__and__Field_Osemiring__0_decl,type,
    class_Ring__and__Field_Osemiring__0: $i > $o ).

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

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__3_decl,type,
    v_sko__Hoare__Mirabelle__Xconseq12__3: $i > $i > $i > $i > $i ).

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

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

thf(t_c_decl,type,
    t_c: $i ).

thf(v_R_decl,type,
    v_R: $i ).

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

thf(c_Fun_Othe__inv__into_decl,type,
    c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).

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

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

thf(c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1_decl,type,
    c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1: $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_Set_Ovimage_decl,type,
    c_Set_Ovimage: $i > $i > $i > $i > $i ).

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

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(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(class_HOL_Ouminus_decl,type,
    class_HOL_Ouminus: $i > $o ).

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

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

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

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__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(c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2_decl,type,
    c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2: $i > $i > $i > $i > $i > $i ).

thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1_decl,type,
    v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1: $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_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1_decl,type,
    c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__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(464,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) @ c_Suc )
        = ( A @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__Diff1_0) ).

thf(2163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) @ c_Suc )
        = ( A @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(109,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__diff__distrib__left_0) ).

thf(1322,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(274,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).

thf(1718,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(664,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(2612,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(721,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/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(2744,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)],[721]) ).

thf(294,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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

thf(1767,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)],[294]) ).

thf(279,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).

thf(1729,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)],[279]) ).

thf(907,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).

thf(3167,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(577,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).

thf(2412,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(322,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).

thf(1840,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)],[322]) ).

thf(326,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).

thf(1850,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)],[326]) ).

thf(584,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(2427,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(1028,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).

thf(3449,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(636,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 )
      | ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
       != ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).

thf(2544,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 )
      | ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
       != ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(540,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/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__commute_0) ).

thf(2331,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)],[540]) ).

thf(523,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).

thf(2295,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(528,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/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

thf(2306,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)],[528]) ).

thf(544,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).

thf(2341,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(440,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 )
      | ~ ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__below__fold1__iff_0) ).

thf(2109,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 )
      | ~ ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(405,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( E @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( A @ ( E @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__graph__permute__diff_0) ).

thf(2031,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( E @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( A @ ( E @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(1007,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_6) ).

thf(3399,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)],[1007]) ).

thf(391,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I21_J_0) ).

thf(1995,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(798,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).

thf(2921,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(1039,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).

thf(3477,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).

thf(599,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(2463,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)],[599]) ).

thf(1006,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).

thf(3397,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( 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)],[1006]) ).

thf(349,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).

thf(1899,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ 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)],[349]) ).

thf(314,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/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__right_0) ).

thf(1818,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)],[314]) ).

thf(98,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/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(1295,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)],[98]) ).

thf(375,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/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).

thf(1956,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)],[375]) ).

thf(373,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( C @ ( E @ c_in ) ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_H_0) ).

thf(1950,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( C @ ( E @ c_in ) ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[373]) ).

thf(205,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).

thf(1549,plain,
    ! [A: $i] :
      ( ( A @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(554,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(2363,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)],[554]) ).

thf(916,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/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

thf(3185,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)],[916]) ).

thf(621,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__inf__insert_0) ).

thf(2512,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) @ 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)],[621]) ).

thf(96,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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

thf(1290,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)],[96]) ).

thf(668,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__commute_0) ).

thf(2622,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)],[668]) ).

thf(570,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ ( G @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_1) ).

thf(2395,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ ( G @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(234,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/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

thf(1618,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)],[234]) ).

thf(901,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( G @ ( F @ ( E @ ( F @ ( tc_bool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I2_J_0) ).

thf(3153,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( G @ ( F @ ( E @ ( F @ ( tc_bool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[901]) ).

thf(655,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 ) )
      | ~ ( A @ ( B @ ( D @ c_in ) ) @ 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/sandbox/benchmark/theBenchmark.p',cls_fold1__strict__below__iff_2) ).

thf(2590,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 ) )
      | ~ ( A @ ( B @ ( D @ c_in ) ) @ 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)],[655]) ).

thf(876,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).

thf(3098,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( 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)],[876]) ).

thf(691,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( A @ ( C @ ( D @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).

thf(2676,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( A @ ( C @ ( D @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( 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)],[691]) ).

thf(880,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Diff__eq_0) ).

thf(3108,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(837,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/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).

thf(3012,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)],[837]) ).

thf(1000,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_0) ).

thf(3382,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).

thf(177,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/sandbox/benchmark/theBenchmark.p',cls_inf__min_0) ).

thf(1486,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)],[177]) ).

thf(862,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).

thf(3072,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[862]) ).

thf(361,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).

thf(1924,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)],[361]) ).

thf(443,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/sandbox/benchmark/theBenchmark.p',cls_Min__antimono_0) ).

thf(2117,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)],[443]) ).

thf(806,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( F @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).

thf(2940,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( F @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(225,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_Orderings_Oord__class_Omin @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__min_0) ).

thf(1596,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)],[225]) ).

thf(749,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 )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__eqI_1) ).

thf(2808,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 )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(194,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

thf(1522,plain,
    tc_nat @ class_Ring__and__Field_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(935,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

thf(3230,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).

thf(564,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__idem_0) ).

thf(2381,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)],[564]) ).

thf(158,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( B @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).

thf(1443,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( B @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[158]) ).

thf(735,axiom,
    tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).

thf(2776,plain,
    tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(310,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/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).

thf(1808,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)],[310]) ).

thf(809,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) )
        = ( A @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( B @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__subset_0) ).

thf(2947,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) )
        = ( A @ ( C @ c_Finite__Set_Ocard ) @ ( A @ ( B @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(214,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/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(1569,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)],[214]) ).

thf(368,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( A @ ( C @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__Compl__subset_0) ).

thf(1939,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( A @ ( C @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(435,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

thf(2099,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(222,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/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).

thf(1591,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)],[222]) ).

thf(762,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

thf(2837,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(38,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__def_0) ).

thf(1142,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(381,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( F @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).

thf(1971,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( F @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(304,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/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(1793,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)],[304]) ).

thf(839,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 ) )
      | ~ ( A @ ( B @ ( D @ c_in ) ) @ 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/sandbox/benchmark/theBenchmark.p',cls_fold1__below__iff_2) ).

thf(3017,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 ) )
      | ~ ( A @ ( B @ ( D @ c_in ) ) @ 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)],[839]) ).

thf(853,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

thf(3049,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( 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)],[853]) ).

thf(290,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/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).

thf(1756,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)],[290]) ).

thf(993,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ hAPP ) )
        = ( B @ ( C @ ( D @ ( A @ ( D @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 ) ) ) ) @ ( A @ hAPP ) ) )
      | ( C @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_2) ).

thf(3365,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ hAPP ) )
        = ( B @ ( C @ ( D @ ( A @ ( D @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 ) ) ) ) @ ( A @ hAPP ) ) )
      | ( C @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).

thf(911,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/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).

thf(3175,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)],[911]) ).

thf(533,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/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

thf(2316,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)],[533]) ).

thf(593,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( G @ ( F @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( B @ ( E @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( E @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( B @ ( A @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( B @ ( B @ ( A @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ofold__inf__insert_0) ).

thf(2448,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( G @ ( F @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( B @ ( E @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( E @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( B @ ( A @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
        = ( E @ ( C @ ( B @ ( B @ ( A @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(587,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Finite__Set_Ofinite ) )
      | ( C @ ( D @ ( E @ c_in ) ) @ hBOOL )
      | ( ( A @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_1) ).

thf(2434,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Finite__Set_Ofinite ) )
      | ( C @ ( D @ ( E @ c_in ) ) @ hBOOL )
      | ( ( A @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(73,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
     != c_Com_Ocom_OSKIP ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).

thf(1233,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
     != c_Com_Ocom_OSKIP ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(651,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/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).

thf(2580,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)],[651]) ).

thf(16,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

thf(1078,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)],[16]) ).

thf(302,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/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(1788,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)],[302]) ).

thf(151,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).

thf(1426,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)],[151]) ).

thf(929,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).

thf(3217,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).

thf(886,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/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).

thf(3120,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)],[886]) ).

thf(1021,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( B @ ( A @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__eq__fold_0) ).

thf(3429,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( B @ ( A @ ( A @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(834,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__le2_0) ).

thf(3004,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)],[834]) ).

thf(407,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
      = D ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__empty_0) ).

thf(2035,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
      = D ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(670,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/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).

thf(2627,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)],[670]) ).

thf(466,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

thf(2168,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(84,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).

thf(1260,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(359,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).

thf(1919,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A
        = ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(388,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( F @ ( E @ ( F @ ( tc_bool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( F @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ( G @ ( F @ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).

thf(1988,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( G @ ( F @ ( E @ ( F @ ( tc_bool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( F @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ( G @ ( F @ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(1013,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ ( G @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_1) ).

thf(3414,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ ( G @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).

thf(292,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).

thf(1761,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)],[292]) ).

thf(789,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( A @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(2901,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( A @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(972,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( D @ ( E @ c_in ) ) @ hBOOL )
      | ( ( A @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( E @ ( B @ hAPP ) @ ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_0) ).

thf(3313,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( D @ ( E @ c_in ) ) @ hBOOL )
      | ( ( A @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( E @ ( B @ hAPP ) @ ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).

thf(11,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

thf(1063,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)],[11]) ).

thf(765,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).

thf(2844,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(188,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/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

thf(1507,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)],[188]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_Orderings_Oord__class_Omax @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__max_0) ).

thf(1222,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)],[69]) ).

thf(819,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(2972,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(783,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/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).

thf(2886,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)],[783]) ).

thf(286,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).

thf(1746,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)],[286]) ).

thf(878,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

thf(3103,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(547,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/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

thf(2348,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)],[547]) ).

thf(987,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Ovimage ) ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).

thf(3350,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Ovimage ) ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

thf(586,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infE_0) ).

thf(2432,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)],[586]) ).

thf(357,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/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

thf(1914,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)],[357]) ).

thf(77,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/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).

thf(1243,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)],[77]) ).

thf(33,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

thf(1127,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)],[33]) ).

thf(300,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( F @ ( C @ ( B @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).

thf(1782,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( F @ ( C @ ( B @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[300]) ).

thf(871,axiom,
    tc_bool @ class_HOL_Ouminus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).

thf(3088,plain,
    tc_bool @ class_HOL_Ouminus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(2,negated_conjecture,
    ~ ( t_a @ ( v_F @ ( v_x @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(1046,plain,
    ~ ( t_a @ ( v_F @ ( v_x @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(969,axiom,
    tc_bool @ class_Finite__Set_Ofinite_Ofinite,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).

thf(3308,plain,
    tc_bool @ class_Finite__Set_Ofinite_Ofinite,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(397,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_0) ).

thf(2010,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(366,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( C @ ( E @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_2) ).

thf(1935,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( C @ ( E @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(957,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = B )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).

thf(3281,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OInf__class_OInf ) )
        = B )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).

thf(1035,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).

thf(3466,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)],[1035]) ).

thf(895,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).

thf(3140,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(277,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 @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).

thf(1724,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 @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[277]) ).

thf(468,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( E @ ( E @ ( F @ ( D @ ( C @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( F @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__graph__insert__swap_0) ).

thf(2173,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( E @ ( E @ ( F @ ( D @ ( C @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( F @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(126,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/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).

thf(1366,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)],[126]) ).

thf(197,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).

thf(1529,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)],[197]) ).

thf(421,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).

thf(2067,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)],[421]) ).

thf(756,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( A @ ( D @ ( A @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).

thf(2825,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( A @ ( D @ ( A @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(753,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 @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).

thf(2819,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 @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(308,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/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).

thf(1803,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)],[308]) ).

thf(451,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( 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 ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

thf(2136,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( 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 ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(352,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/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(1904,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)],[352]) ).

thf(236,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/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

thf(1623,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)],[236]) ).

thf(81,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(1254,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(920,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/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

thf(3195,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)],[920]) ).

thf(250,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).

thf(1660,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(543,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

thf(2339,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ 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)],[543]) ).

thf(984,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).

thf(3342,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).

thf(335,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/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

thf(1871,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)],[335]) ).

thf(858,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(3061,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(706,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(2708,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(899,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(3148,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)],[899]) ).

thf(190,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).

thf(1511,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)],[190]) ).

thf(317,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).

thf(1826,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[317]) ).

thf(319,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/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).

thf(1832,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)],[319]) ).

thf(988,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).

thf(3353,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)],[988]) ).

thf(447,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/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

thf(2126,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)],[447]) ).

thf(850,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).

thf(3043,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(703,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).

thf(2703,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(949,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/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

thf(3263,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)],[949]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).

thf(1287,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(931,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/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).

thf(3221,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)],[931]) ).

thf(660,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).

thf(2603,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(539,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
        = ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

thf(2328,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
        = ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(796,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( B @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( B @ ( A @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__eq__fold_0) ).

thf(2916,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( B @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( B @ ( A @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(751,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Un_0) ).

thf(2814,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(387,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_Min__insert_0) ).

thf(1985,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( 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)],[387]) ).

thf(883,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).

thf(3116,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(687,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
       != ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__card__imp__inj__on_0) ).

thf(2667,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
       != ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(106,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( 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_OgreaterThanAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greaterThanAtMost_0) ).

thf(1313,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( 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_OgreaterThanAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(92,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/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).

thf(1279,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)],[92]) ).

thf(474,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/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(2185,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)],[474]) ).

thf(218,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).

thf(1577,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)],[218]) ).

thf(872,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ( ( tc_nat @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Osetsum ) ) ) )
        = ( D @ ( A @ hAPP ) @ ( tc_nat @ ( B @ ( C @ ( A @ c_Finite__Set_Osetsum ) ) ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__nat_0) ).

thf(3089,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ( ( tc_nat @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Osetsum ) ) ) )
        = ( D @ ( A @ hAPP ) @ ( tc_nat @ ( B @ ( C @ ( A @ c_Finite__Set_Osetsum ) ) ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(611,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).

thf(2488,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(722,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( G @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ ( G @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ ( D @ c_Com_Ocom_OSemi ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comp_0) ).

thf(2745,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( G @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ ( G @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( E @ ( D @ c_Com_Ocom_OSemi ) @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(648,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/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

thf(2571,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)],[648]) ).

thf(551,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).

thf(2356,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(203,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( B @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__fold__inf_0) ).

thf(1545,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( B @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(360,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).

thf(1922,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(708,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ 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__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).

thf(2713,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ 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__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(40,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

thf(1147,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)],[40]) ).

thf(174,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/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).

thf(1479,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)],[174]) ).

thf(29,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).

thf(1115,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)],[29]) ).

thf(364,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).

thf(1931,plain,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(461,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( A @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

thf(2158,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = ( A @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(243,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).

thf(1641,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(296,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/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

thf(1773,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)],[296]) ).

thf(769,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(2852,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(567,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/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(2388,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)],[567]) ).

thf(24,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
       != ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).

thf(1100,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
       != ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(951,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/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).

thf(3268,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)],[951]) ).

thf(325,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).

thf(1847,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)],[325]) ).

thf(996,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(3374,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( 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)],[996]) ).

thf(1001,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__inf__le__inf_0) ).

thf(3385,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).

thf(1034,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).

thf(3463,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).

thf(131,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/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).

thf(1379,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)],[131]) ).

thf(19,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

thf(1087,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(191,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image_0) ).

thf(1514,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(108,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/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

thf(1319,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)],[108]) ).

thf(268,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/sandbox/benchmark/theBenchmark.p',cls_dual__semilattice_0) ).

thf(1704,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)],[268]) ).

thf(344,axiom,
    ! [A: $i] : ( A @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

thf(1890,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)],[344]) ).

thf(119,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

thf(1347,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)],[119]) ).

thf(215,axiom,
    tc_nat @ class_Lattices_Oupper__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

thf(1572,plain,
    tc_nat @ class_Lattices_Oupper__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(284,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/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).

thf(1741,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)],[284]) ).

thf(869,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ ( E @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( D @ ( B @ ( A @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( D @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__inj__on__le_0) ).

thf(3084,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ ( E @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( D @ ( B @ ( A @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( D @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(838,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/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).

thf(3014,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)],[838]) ).

thf(715,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
       != ( G @ ( F @ ( E @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).

thf(2730,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = F )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
       != ( G @ ( F @ ( E @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(526,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/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(2301,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)],[526]) ).

thf(181,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/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).

thf(1494,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)],[181]) ).

thf(827,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/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(2989,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)],[827]) ).

thf(378,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/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(1963,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)],[378]) ).

thf(337,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
       != ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).

thf(1875,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
       != ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(298,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/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).

thf(1778,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)],[298]) ).

thf(471,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_0) ).

thf(2178,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(431,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ 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/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).

thf(2090,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ 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)],[431]) ).

thf(27,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).

thf(1109,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(905,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).

thf(3163,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(961,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(3290,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).

thf(736,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_5) ).

thf(2777,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)],[736]) ).

thf(178,axiom,
    tc_nat @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(1489,plain,
    tc_nat @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(810,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infI1_0) ).

thf(2950,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)],[810]) ).

thf(146,axiom,
    ! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).

thf(1415,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(101,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).

thf(1302,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)],[101]) ).

thf(252,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oab__semigroup__idem__mult__inf_0) ).

thf(1664,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)],[252]) ).

thf(438,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Ominus )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).

thf(2105,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Ominus )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(864,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/sandbox/benchmark/theBenchmark.p',cls_empty_0) ).

thf(3075,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)],[864]) ).

thf(129,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).

thf(1373,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(831,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/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(2996,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)],[831]) ).

thf(355,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).

thf(1911,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(963,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/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

thf(3295,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)],[963]) ).

thf(738,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/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

thf(2782,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)],[738]) ).

thf(148,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

thf(1418,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)],[148]) ).

thf(594,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( A @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(2451,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( A @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(496,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/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(2236,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)],[496]) ).

thf(780,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_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).

thf(2880,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_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(259,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/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(1682,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)],[259]) ).

thf(36,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_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( 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_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).

thf(1136,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_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( 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_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(1024,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/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).

thf(3438,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)],[1024]) ).

thf(332,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

thf(1864,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(445,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/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

thf(2122,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)],[445]) ).

thf(800,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/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

thf(2925,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)],[800]) ).

thf(384,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/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(1978,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)],[384]) ).

thf(257,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ c_Suc @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).

thf(1677,plain,
    ! [B: $i,A: $i] :
      ( ( B @ c_Suc @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(634,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

thf(2540,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)],[634]) ).

thf(55,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_Orderings_Oord__class_Omin @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).

thf(1183,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)],[55]) ).

thf(424,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).

thf(2073,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(417,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).

thf(2058,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)],[417]) ).

thf(517,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( D @ ( D @ ( F @ ( E @ ( C @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( D @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( E @ ( C @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( F @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__graph__permute__diff_0) ).

thf(2281,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( D @ ( D @ ( F @ ( E @ ( C @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( D @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( E @ ( C @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( F @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(342,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ c_Suc @ ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).

thf(1886,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ c_Suc @ ( B @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(196,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

thf(1526,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(154,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/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).

thf(1433,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)],[154]) ).

thf(437,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).

thf(2103,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(227,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/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(1600,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)],[227]) ).

thf(265,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/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).

thf(1697,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)],[265]) ).

thf(1010,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).

thf(3406,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).

thf(212,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( C @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).

thf(1564,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( C @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(998,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(3378,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( D @ c_in ) ) @ hBOOL )
      | ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( 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)],[998]) ).

thf(1003,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( C @ ( E @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_2) ).

thf(3389,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( C @ ( E @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).

thf(816,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oinsert ) ) )
      = ( B @ ( C @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

thf(2964,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oinsert ) ) )
      = ( B @ ( C @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(556,axiom,
    tc_bool @ class_Lattices_Odistrib__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

thf(2367,plain,
    tc_bool @ class_Lattices_Odistrib__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(588,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( B @ c_Finite__Set_Ocard ) @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__le_0) ).

thf(2437,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( B @ c_Finite__Set_Ocard ) @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(347,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/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

thf(1896,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)],[347]) ).

thf(476,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/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).

thf(2190,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)],[476]) ).

thf(1017,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/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

thf(3421,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)],[1017]) ).

thf(160,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).

thf(1447,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(609,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/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

thf(2483,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)],[609]) ).

thf(14,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

thf(1072,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)],[14]) ).

thf(629,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/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).

thf(2530,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)],[629]) ).

thf(626,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( B @ ( A @ ( C @ c_Fun_Oinj__on ) ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).

thf(2523,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( B @ ( A @ ( C @ c_Fun_Oinj__on ) ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).

thf(1796,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ 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)],[305]) ).

thf(138,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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

thf(1394,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)],[138]) ).

thf(733,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).

thf(2772,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)],[733]) ).

thf(499,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/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).

thf(2242,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)],[499]) ).

thf(118,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/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(1345,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)],[118]) ).

thf(933,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition2_0) ).

thf(3226,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).

thf(370,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).

thf(1943,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(61,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/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).

thf(1201,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)],[61]) ).

thf(915,axiom,
    tc_bool @ class_HOL_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(3184,plain,
    tc_bool @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(653,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( C @ ( E @ ( D @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( E @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__subtractf_0) ).

thf(2586,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( C @ ( E @ ( D @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( E @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(782,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/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

thf(2884,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)],[782]) ).

thf(1023,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/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

thf(3435,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)],[1023]) ).

thf(812,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/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(2954,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)],[812]) ).

thf(799,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) @ c_Suc ) )
      | ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_5) ).

thf(2922,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) @ c_Suc ) )
      | ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).

thf(1206,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(263,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).

thf(1691,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)],[263]) ).

thf(103,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/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).

thf(1306,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)],[103]) ).

thf(60,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).

thf(1199,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(115,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(1338,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)],[115]) ).

thf(1015,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 ) )
      | ~ ( C @ ( D @ ( E @ c_in ) ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ofold1__belowI_0) ).

thf(3418,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 ) )
      | ~ ( C @ ( D @ ( E @ c_in ) ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).

thf(649,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__empty_0) ).

thf(2574,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(156,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(1438,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)],[156]) ).

thf(908,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/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).

thf(3169,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)],[908]) ).

thf(950,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(3265,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).

thf(412,axiom,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Orderings_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).

thf(2047,plain,
    ! [A: $i] :
      ( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Orderings_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(974,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/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

thf(3318,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)],[974]) ).

thf(105,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/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

thf(1311,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)],[105]) ).

thf(855,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ 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_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

thf(3054,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ 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_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(428,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_in ) ) @ hBOOL )
      | ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).

thf(2083,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_in ) ) @ hBOOL )
      | ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(282,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/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

thf(1736,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)],[282]) ).

thf(614,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).

thf(2496,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(791,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( A @ ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).

thf(2905,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( A @ ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(334,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/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).

thf(1868,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)],[334]) ).

thf(418,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( E @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( A @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__insert__swap_0) ).

thf(2061,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( E @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( A @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(241,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/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).

thf(1636,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)],[241]) ).

thf(7,negated_conjecture,
    ( ~ ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( t_a @ ( v_F @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( t_a @ ( v_Q_H @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( t_a @ ( v_c0 @ ( t_a @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( v_P_H @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
    | ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( t_a @ ( v_F @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( t_a @ ( v_Q @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( t_a @ ( v_c0 @ ( t_a @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( v_P @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).

thf(1047,plain,
    ( ~ ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( t_a @ ( v_F @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( t_a @ ( v_Q_H @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( t_a @ ( v_c0 @ ( t_a @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( v_P_H @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
    | ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( t_a @ ( v_F @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( t_a @ ( v_Q @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( t_a @ ( v_c0 @ ( t_a @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( v_P @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(847,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/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).

thf(3037,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)],[847]) ).

thf(9,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).

thf(1057,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)],[9]) ).

thf(654,axiom,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).

thf(2589,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)],[654]) ).

thf(134,axiom,
    tc_nat @ class_Lattices_Odistrib__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).

thf(1387,plain,
    tc_nat @ class_Lattices_Odistrib__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(21,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

thf(1091,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)],[21]) ).

thf(659,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/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).

thf(2601,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)],[659]) ).

thf(502,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/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(2249,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)],[502]) ).

thf(657,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( D @ ( C @ c_Finite__Set_Osetsum ) ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( E @ ( D @ ( E @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__right__distrib_0) ).

thf(2596,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( D @ ( C @ c_Finite__Set_Osetsum ) ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( E @ ( D @ ( E @ ( A @ ( A @ ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(82,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( 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_OatLeastLessThan ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__atLeastLessThan_0) ).

thf(1255,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( 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_OatLeastLessThan ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(288,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).

thf(1751,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[288]) ).

thf(253,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/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).

thf(1666,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)],[253]) ).

thf(818,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).

thf(2969,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(628,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).

thf(2528,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(90,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/sandbox/benchmark/theBenchmark.p',cls_Int__atLeastAtMost_0) ).

thf(1274,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)],[90]) ).

thf(690,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).

thf(2673,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(509,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).

thf(2264,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(576,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( A @ c_in ) ) @ 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/sandbox/benchmark/theBenchmark.p',cls_vimage__const_1) ).

thf(2409,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( A @ c_in ) ) @ 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)],[576]) ).

thf(716,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(2733,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(117,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/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).

thf(1343,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)],[117]) ).

thf(643,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/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__ac_I1_J_0) ).

thf(2560,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)],[643]) ).

thf(122,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).

thf(1355,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)],[122]) ).

thf(219,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

thf(1580,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(67,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).

thf(1217,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)],[67]) ).

thf(456,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infI2_0) ).

thf(2147,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)],[456]) ).

thf(939,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(3239,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(861,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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(3069,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)],[861]) ).

thf(995,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A @ ( B @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).

thf(3371,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A @ ( B @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(805,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_fold1__insert_0) ).

thf(2937,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( 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)],[805]) ).

thf(316,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/sandbox/benchmark/theBenchmark.p',cls_max__lattice_0) ).

thf(1824,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)],[316]) ).

thf(458,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/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).

thf(2150,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)],[458]) ).

thf(128,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).

thf(1370,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(449,axiom,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).

thf(2132,plain,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(578,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/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

thf(2414,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)],[578]) ).

thf(944,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/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).

thf(3250,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)],[944]) ).

thf(959,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
      = ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

thf(3286,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
      = ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(210,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/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).

thf(1560,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)],[210]) ).

thf(777,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).

thf(2873,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)],[777]) ).

thf(321,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/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

thf(1837,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)],[321]) ).

thf(688,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).

thf(2670,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(605,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(2477,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(964,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).

thf(3297,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).

thf(53,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/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).

thf(1178,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)],[53]) ).

thf(343,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/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).

thf(1888,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)],[343]) ).

thf(261,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/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).

thf(1687,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)],[261]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).

thf(1159,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(472,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

thf(2181,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(441,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff2_0) ).

thf(2112,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(216,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).

thf(1573,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)],[216]) ).

thf(732,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
      | ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).

thf(2769,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
      | ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(814,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).

thf(2958,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(150,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

thf(1423,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)],[150]) ).

thf(1009,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

thf(3403,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).

thf(380,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( C @ ( E @ ( A @ ( A @ ( D @ ( D @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_Finite__Set_Osetsum ) ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__left__distrib_0) ).

thf(1968,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( A @ ( D @ ( C @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( C @ ( E @ ( A @ ( A @ ( D @ ( D @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_Finite__Set_Osetsum ) ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

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

thf(2565,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( A @ ( B @ ( D @ c_in ) ) @ hBOOL )
      | ( A @ ( B @ c_Finite__Set_Ocard ) @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(921,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I16_J_0) ).

thf(3198,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( 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)],[921]) ).

thf(685,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( B @ c_Finite__Set_Ocard ) @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image__le_0) ).

thf(2663,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( B @ c_Finite__Set_Ocard ) @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(208,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/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

thf(1555,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)],[208]) ).

thf(757,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).

thf(2826,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(538,axiom,
    tc_bool @ class_Orderings_Obot,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(2327,plain,
    tc_bool @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(486,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).

thf(2213,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)],[486]) ).

thf(485,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).

thf(2211,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(143,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( B @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(1407,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( B @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
       != ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(637,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).

thf(2547,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(545,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__eq_0) ).

thf(2344,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(93,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/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(1281,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)],[93]) ).

thf(720,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).

thf(2741,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(240,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).

thf(1634,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(137,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/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).

thf(1392,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)],[137]) ).

thf(492,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/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).

thf(2228,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)],[492]) ).

thf(681,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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_escape_0) ).

thf(2653,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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(26,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).

thf(1106,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)],[26]) ).

thf(141,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/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).

thf(1402,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)],[141]) ).

thf(120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).

thf(1350,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(386,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 )
      | ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

thf(1983,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 )
      | ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(442,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).

thf(2115,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(887,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_4) ).

thf(3122,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)],[887]) ).

thf(31,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

thf(1121,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)],[31]) ).

thf(650,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( 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 ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_1) ).

thf(2577,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( 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 ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(71,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).

thf(1227,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)],[71]) ).

thf(699,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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(2694,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)],[699]) ).

thf(255,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

thf(1672,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)],[255]) ).

thf(885,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_Finite__Set_Ofold__graph ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).

thf(3119,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_Finite__Set_Ofold__graph ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(866,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).

thf(3078,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(938,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
      | ( D @ ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__range__imageI_0) ).

thf(3237,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
      | ( D @ ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).

thf(30,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).

thf(1118,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(511,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/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(2268,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)],[511]) ).

thf(833,axiom,
    ! [A: $i] :
      ( ( ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).

thf(3001,plain,
    ! [A: $i] :
      ( ( ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(615,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(2498,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(201,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/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

thf(1541,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)],[201]) ).

thf(1041,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).

thf(3482,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( 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)],[1041]) ).

thf(622,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).

thf(2515,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(946,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ ( F @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( C @ ( E @ c_Fun_Oinj__on ) ) ) )
      | ~ ( A @ ( B @ ( D @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
        = ( D @ ( C @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__bij__eq_0) ).

thf(3254,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ ( F @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( D @ ( C @ ( E @ c_Fun_Oinj__on ) ) ) )
      | ~ ( A @ ( B @ ( D @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
        = ( D @ ( C @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).

thf(562,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

thf(2377,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(746,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_2) ).

thf(2801,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)],[746]) ).

thf(198,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).

thf(1534,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)],[198]) ).

thf(374,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
      | ( A
        = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).

thf(1953,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
      | ( A
        = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(695,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

thf(2685,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(764,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/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Ofold1__Un2_0) ).

thf(2841,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)],[764]) ).

thf(111,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(1328,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)],[111]) ).

thf(698,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(2692,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(183,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/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(1498,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)],[183]) ).

thf(338,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).

thf(1878,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)],[338]) ).

thf(672,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
       != ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).

thf(2631,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
       != ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(713,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
        = ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_1) ).

thf(2724,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
        = ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(771,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oless__infI2_0) ).

thf(2858,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)],[771]) ).

thf(912,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_Max__insert_0) ).

thf(3176,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( 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)],[912]) ).

thf(139,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).

thf(1397,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)],[139]) ).

thf(213,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 @ ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).

thf(1567,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 @ ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[213]) ).

thf(897,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(3143,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).

thf(124,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

thf(1361,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)],[124]) ).

thf(926,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/sandbox/benchmark/theBenchmark.p',cls_psubset__card__mono_0) ).

thf(3210,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)],[926]) ).

thf(759,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( B @ c_Finite__Set_Ocard ) @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__less_0) ).

thf(2830,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( B @ c_Finite__Set_Ocard ) @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(775,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( E @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).

thf(2868,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( E @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( 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)],[775]) ).

thf(15,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).

thf(1075,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)],[15]) ).

thf(427,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I11_J_0) ).

thf(2080,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( 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)],[427]) ).

thf(367,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(1937,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(311,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/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).

thf(1810,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)],[311]) ).

thf(66,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).

thf(1214,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(244,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).

thf(1644,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)],[244]) ).

thf(598,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ononempty__iff_2) ).

thf(2460,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(180,axiom,
    tc_nat @ class_Orderings_Obot,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

thf(1493,plain,
    tc_nat @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(745,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

thf(2798,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(896,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Compl_0) ).

thf(3141,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ 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)],[896]) ).

thf(779,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ c_Set_Oimage ) ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__onto_0) ).

thf(2877,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ c_Set_Oimage ) ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(402,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__left__commute_0) ).

thf(2023,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)],[402]) ).

thf(977,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(3326,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).

thf(536,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/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).

thf(2323,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)],[536]) ).

thf(913,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).

thf(3179,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).

thf(874,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/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

thf(3094,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)],[874]) ).

thf(166,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

thf(1461,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)],[166]) ).

thf(1025,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( B @ c_in ) ) @ hBOOL )
      | ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
        = ( E @ ( E @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( F @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).

thf(3441,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( B @ c_in ) ) @ hBOOL )
      | ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
        = ( E @ ( E @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( F @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).

thf(531,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ( A @ ( B @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).

thf(2312,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ( A @ ( B @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(596,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ 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/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).

thf(2455,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ 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)],[596]) ).

thf(415,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Obounded__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(2053,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)],[415]) ).

thf(478,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).

thf(2196,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(498,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(2240,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( D @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(323,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).

thf(1842,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)],[323]) ).

thf(639,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/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

thf(2551,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)],[639]) ).

thf(429,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).

thf(2085,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ 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)],[429]) ).

thf(231,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

thf(1612,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)],[231]) ).

thf(679,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/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

thf(2649,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)],[679]) ).

thf(822,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).

thf(2978,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)],[822]) ).

thf(603,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/sandbox/benchmark/theBenchmark.p',cls_Min__Un_0) ).

thf(2472,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)],[603]) ).

thf(941,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 ) )
        = ( C @ ( B @ ( A @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__Inf__fold__inf_0) ).

thf(3242,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 ) )
        = ( C @ ( B @ ( A @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).

thf(519,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/sandbox/benchmark/theBenchmark.p',cls_Max__Un_0) ).

thf(2285,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)],[519]) ).

thf(857,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(3059,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(87,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/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).

thf(1266,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)],[87]) ).

thf(382,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oless__infI1_0) ).

thf(1974,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)],[382]) ).

thf(768,axiom,
    tc_bool @ class_HOL_Ominus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).

thf(2851,plain,
    tc_bool @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(618,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).

thf(2505,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)],[618]) ).

thf(395,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

thf(2006,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)],[395]) ).

thf(306,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/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

thf(1799,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)],[306]) ).

thf(372,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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(1947,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)],[372]) ).

thf(327,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/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__sup_0) ).

thf(1852,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)],[327]) ).

thf(863,axiom,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).

thf(3074,plain,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( 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)],[863]) ).

thf(513,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(2272,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(453,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBS ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).

thf(2140,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBS ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(558,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_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

thf(2370,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_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(297,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/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).

thf(1776,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)],[297]) ).

thf(86,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).

thf(1263,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)],[86]) ).

thf(803,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( F @ c_Finite__Set_Ofinite ) )
      | ( C @ ( F @ ( E @ c_in ) ) @ hBOOL )
      | ( ( C @ ( F @ ( E @ c_Set_Oinsert ) ) @ ( D @ ( C @ ( A @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) @ hAPP ) @ hAPP ) )
        = ( F @ ( D @ ( C @ ( A @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) @ hAPP ) @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__image__insert_0) ).

thf(2932,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( F @ c_Finite__Set_Ofinite ) )
      | ( C @ ( F @ ( E @ c_in ) ) @ hBOOL )
      | ( ( C @ ( F @ ( E @ c_Set_Oinsert ) ) @ ( D @ ( C @ ( A @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) @ hAPP ) @ hAPP ) )
        = ( F @ ( D @ ( C @ ( A @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__image ) ) ) @ hAPP ) @ hAPP ) @ ( 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)],[803]) ).

thf(221,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/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

thf(1588,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)],[221]) ).

thf(42,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).

thf(1150,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)],[42]) ).

thf(173,axiom,
    ! [A: $i] : ( A @ c_Suc @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).

thf(1478,plain,
    ! [A: $i] : ( A @ c_Suc @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(624,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/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

thf(2519,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)],[624]) ).

thf(632,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).

thf(2536,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(99,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/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).

thf(1297,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)],[99]) ).

thf(889,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(3126,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(693,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).

thf(2681,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(200,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/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).

thf(1539,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)],[200]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).

thf(1456,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(600,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/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(2465,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)],[600]) ).

thf(10,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

thf(1060,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)],[10]) ).

thf(152,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/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__inf_0) ).

thf(1429,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)],[152]) ).

thf(943,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).

thf(3247,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Complete__Lattice_OInf__class_OInf ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(1011,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/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(3409,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)],[1011]) ).

thf(773,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ ( B @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 ) ) ) ) )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_3) ).

thf(2862,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ ( B @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 ) ) ) ) )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(731,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/sandbox/benchmark/theBenchmark.p',cls_fold1__Un_0) ).

thf(2766,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)],[731]) ).

thf(414,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/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(2052,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)],[414]) ).

thf(608,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/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

thf(2482,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)],[608]) ).

thf(78,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).

thf(1246,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)],[78]) ).

thf(273,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/sandbox/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).

thf(1715,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)],[273]) ).

thf(980,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/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

thf(3333,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)],[980]) ).

thf(868,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(3083,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)],[868]) ).

thf(922,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/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).

thf(3201,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)],[922]) ).

thf(291,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/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).

thf(1759,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)],[291]) ).

thf(1030,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__le_0) ).

thf(3454,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(113,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/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

thf(1333,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)],[113]) ).

thf(481,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oupper__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__sup__insert_0) ).

thf(2203,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) )
        = ( D @ ( B @ ( A @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) @ 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)],[481]) ).

thf(729,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/sandbox/benchmark/theBenchmark.p',cls_fold1__Un2_0) ).

thf(2761,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)],[729]) ).

thf(483,axiom,
    tc_bool @ class_Lattices_Obounded__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

thf(2208,plain,
    tc_bool @ class_Lattices_Obounded__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(410,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).

thf(2043,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(910,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/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).

thf(3173,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)],[910]) ).

thf(50,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).

thf(1170,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(168,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__greatest_0) ).

thf(1466,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)],[168]) ).

thf(49,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(1167,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)],[49]) ).

thf(677,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( E @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).

thf(2645,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( E @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(666,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
        = ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff2_1) ).

thf(2617,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
        = ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(582,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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(2423,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)],[582]) ).

thf(793,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( E @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( A @ ( E @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold__graph__insert__swap_0) ).

thf(2909,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( E @ ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( A @ ( E @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(673,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( C @ ( E @ ( D @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( E @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__addf_0) ).

thf(2634,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( E @ ( A @ ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( C @ ( E @ ( D @ c_Finite__Set_Osetsum ) ) ) @ ( A @ ( C @ ( E @ ( 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)],[673]) ).

thf(724,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(2749,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(329,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 @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).

thf(1857,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 @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[329]) ).

thf(968,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/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

thf(3306,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)],[968]) ).

thf(8,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

thf(1054,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)],[8]) ).

thf(975,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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 )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).

thf(3321,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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 )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).

thf(557,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq2_0) ).

thf(2368,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(743,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ 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/sandbox/benchmark/theBenchmark.p',cls_Inf__binary_0) ).

thf(2793,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ 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)],[743]) ).

thf(918,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/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

thf(3190,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)],[918]) ).

thf(353,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).

thf(1906,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( D @ ( C @ ( E @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[353]) ).

thf(393,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition_0) ).

thf(2001,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(278,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/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).

thf(1727,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)],[278]) ).

thf(470,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/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(2176,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)],[470]) ).

thf(522,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_HOL_Ominus ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).

thf(2292,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( v_x @ ( C @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ hAPP ) )
        = ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_HOL_Ominus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(849,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

thf(3042,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(204,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

thf(1548,plain,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(954,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_1) ).

thf(3274,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).

thf(786,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

thf(2894,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(561,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).

thf(2376,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Nitpick_Osko__Nitpick__XEx1__def__1__3 ) @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(239,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup__top_0) ).

thf(1631,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(80,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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

thf(1251,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)],[80]) ).

thf(293,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).

thf(1764,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(891,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
     != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(3130,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
     != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).

thf(376,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).

thf(1959,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(641,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(2556,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(25,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

thf(1103,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)],[25]) ).

thf(990,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/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

thf(3358,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)],[990]) ).

thf(504,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/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__left__commute_0) ).

thf(2253,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)],[504]) ).

thf(406,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/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).

thf(2033,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)],[406]) ).

thf(457,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( c_Com_Ocom_OSKIP @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).

thf(2149,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( c_Com_Ocom_OSKIP @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(947,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ 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/sandbox/benchmark/theBenchmark.p',cls_Inf__insert_0) ).

thf(3257,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ 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)],[947]) ).

thf(710,axiom,
    ( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
    = ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).

thf(2717,plain,
    ( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
    = ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(68,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).

thf(1219,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(903,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

thf(3158,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

thf(507,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/sandbox/benchmark/theBenchmark.p',cls_card__psubset_0) ).

thf(2260,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)],[507]) ).

thf(44,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).

thf(1154,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(1002,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(3387,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).

thf(714,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/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(2727,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)],[714]) ).

thf(358,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/sandbox/benchmark/theBenchmark.p',cls_add__eq__inf__sup_0) ).

thf(1916,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)],[358]) ).

thf(937,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/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).

thf(3234,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)],[937]) ).

thf(741,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/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(2789,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)],[741]) ).

thf(627,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_in ) ) @ hBOOL )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).

thf(2525,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( E @ c_in ) ) @ hBOOL )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(1037,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ 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/sandbox/benchmark/theBenchmark.p',cls_fold1__belowI_0) ).

thf(3472,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ 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)],[1037]) ).

thf(399,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 )
      | ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
       != ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(2016,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 )
      | ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
       != ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(748,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/sandbox/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).

thf(2806,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)],[748]) ).

thf(1032,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/sandbox/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).

thf(3458,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)],[1032]) ).

thf(193,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).

thf(1520,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)],[193]) ).

thf(32,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

thf(1124,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)],[32]) ).

thf(450,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/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

thf(2134,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)],[450]) ).

thf(491,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) )
        = ( A @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__singleton__if_1) ).

thf(2225,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) )
        = ( A @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(341,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/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

thf(1884,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)],[341]) ).

thf(742,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( 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 ) ) @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_escape_1) ).

thf(2791,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( 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 ) ) @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(940,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).

thf(3240,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).

thf(475,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

thf(2188,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(824,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(2981,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(569,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_bool @ ( A @ tc_fun ) @ 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/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_0) ).

thf(2393,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_bool @ ( A @ tc_fun ) @ 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)],[569]) ).

thf(870,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Oboolean__algebra )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).

thf(3086,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Oboolean__algebra )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(247,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

thf(1652,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)],[247]) ).

thf(867,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/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

thf(3081,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)],[867]) ).

thf(363,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).

thf(1929,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)],[363]) ).

thf(135,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).

thf(1388,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[135]) ).

thf(953,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/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).

thf(3272,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)],[953]) ).

thf(404,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_bool @ ( A @ tc_fun ) @ 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/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_1) ).

thf(2029,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_bool @ ( A @ tc_fun ) @ 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)],[404]) ).

thf(270,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).

thf(1707,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(718,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(2738,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)],[718]) ).

thf(804,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( D @ ( C @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( D @ ( D @ tc_Hoare__Mirabelle_Otriple @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).

thf(2935,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( D @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ~ ( D @ ( C @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( D @ ( D @ tc_Hoare__Mirabelle_Otriple @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(416,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).

thf(2055,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(465,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq2_1) ).

thf(2166,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(597,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

thf(2457,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)],[597]) ).

thf(83,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/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

thf(1258,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)],[83]) ).

thf(967,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( G @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( E @ ( F @ c_in ) ) @ hBOOL )
      | ( D @ ( F @ ( B @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ ( C @ ( B @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ofold__inf__le__inf_0) ).

thf(3304,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( G @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( C @ ( E @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( E @ ( F @ c_in ) ) @ hBOOL )
      | ( D @ ( F @ ( B @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ ( C @ ( B @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).

thf(167,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).

thf(1464,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(966,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) )
      = ( D @ ( C @ ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__composition_0) ).

thf(3302,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) )
      = ( D @ ( C @ ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).

thf(70,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/sandbox/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).

thf(1224,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)],[70]) ).

thf(552,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).

thf(2358,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)],[552]) ).

thf(256,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 @ ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).

thf(1675,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 @ ( D @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[256]) ).

thf(37,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).

thf(1139,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(185,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

thf(1503,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(477,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).

thf(2193,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(841,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

thf(3023,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)],[841]) ).

thf(254,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/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).

thf(1669,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)],[254]) ).

thf(884,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).

thf(3118,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(489,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( B @ ( A @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__eq__fold__idem_0) ).

thf(2220,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( B @ ( A @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(785,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/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(2891,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)],[785]) ).

thf(89,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).

thf(1271,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(529,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(2308,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(925,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/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

thf(3208,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)],[925]) ).

thf(333,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
       != ( D @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(1865,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
       != ( D @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(983,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/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).

thf(3340,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)],[983]) ).

thf(75,axiom,
    ! [B: $i,A: $i] : ( A @ c_Suc @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).

thf(1239,plain,
    ! [B: $i,A: $i] : ( A @ c_Suc @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(590,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).

thf(2442,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(728,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/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).

thf(2759,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)],[728]) ).

thf(583,axiom,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).

thf(2425,plain,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(1014,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( C @ ( E @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).

thf(3416,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( C @ ( E @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(620,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).

thf(2510,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(553,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

thf(2361,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(625,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).

thf(2521,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(64,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).

thf(1209,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(692,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).

thf(2679,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[692]) ).

thf(674,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( A @ ( B @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__the__inv__into__f_0) ).

thf(2637,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) @ hBOOL )
      | ( ( E @ ( D @ ( C @ ( A @ ( B @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(734,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( B @ ( D @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).

thf(2774,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( B @ ( D @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(3,negated_conjecture,
    t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ ( v_Q_H @ hAPP ) @ ( v_x @ ( v_c0 @ hAPP ) @ ( v_x @ ( v_P_H @ hAPP ) @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(1048,plain,
    t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ ( v_Q_H @ hAPP ) @ ( v_x @ ( v_c0 @ hAPP ) @ ( v_x @ ( v_P_H @ hAPP ) @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(365,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/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(1933,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)],[365]) ).

thf(879,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_Hoare__Mirabelle_Otriple @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).

thf(3106,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_Hoare__Mirabelle_Otriple @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).

thf(276,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).

thf(1722,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)],[276]) ).

thf(763,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).

thf(2839,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(894,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/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(3138,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)],[894]) ).

thf(130,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/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

thf(1376,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)],[130]) ).

thf(904,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ( ( B @ ( B @ ( A @ hAPP ) @ hAPP ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Omult__idem_0) ).

thf(3160,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)],[904]) ).

thf(58,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/sandbox/benchmark/theBenchmark.p',cls_linorder__class_OMin__def__raw_0) ).

thf(1194,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)],[58]) ).

thf(546,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).

thf(2346,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( 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)],[546]) ).

thf(676,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(2642,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)],[676]) ).

thf(902,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/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).

thf(3155,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)],[902]) ).

thf(579,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 ) )
      | ( B @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__insert_0) ).

thf(2415,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 ) )
      | ( B @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( 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)],[579]) ).

thf(826,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
      | ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_1) ).

thf(2987,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
      | ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).

thf(346,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).

thf(1894,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(613,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/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Omult__left__idem_0) ).

thf(2493,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)],[613]) ).

thf(434,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).

thf(2097,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(952,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).

thf(3270,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).

thf(501,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ( ( tc_nat @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Osetsum ) ) ) )
        = ( tc_nat @ ( B @ ( C @ ( A @ c_Finite__Set_Osetsum ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__nat_1) ).

thf(2246,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( D @ c_in ) ) @ hBOOL )
      | ( ( tc_nat @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Osetsum ) ) ) )
        = ( tc_nat @ ( B @ ( C @ ( A @ c_Finite__Set_Osetsum ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(228,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/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

thf(1603,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)],[228]) ).

thf(525,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).

thf(2299,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(807,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/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

thf(2943,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)],[807]) ).

thf(808,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

thf(2945,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(5,negated_conjecture,
    ~ ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ ( v_Q @ hAPP ) @ ( v_x @ ( v_c0 @ hAPP ) @ ( v_x @ ( v_P @ hAPP ) @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(1043,plain,
    ~ ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ ( v_Q @ hAPP ) @ ( v_x @ ( v_c0 @ hAPP ) @ ( v_x @ ( v_P @ hAPP ) @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(307,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/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

thf(1801,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)],[307]) ).

thf(262,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(1690,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(860,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).

thf(3066,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(787,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_0) ).

thf(2896,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(420,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/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).

thf(2065,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)],[420]) ).

thf(52,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).

thf(1175,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(1031,axiom,
    ( ( v_R @ ( t_c @ ( t_b @ ( t_a @ ( v_Q @ ( v_P @ c_COMBB ) ) ) ) @ hAPP ) )
    = ( v_R @ ( v_Q @ hAPP ) @ ( v_P @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def__raw_0) ).

thf(3456,plain,
    ( ( v_R @ ( t_c @ ( t_b @ ( t_a @ ( v_Q @ ( v_P @ c_COMBB ) ) ) ) @ hAPP ) )
    = ( v_R @ ( v_Q @ hAPP ) @ ( v_P @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).

thf(930,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/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).

thf(3219,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)],[930]) ).

thf(170,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).

thf(1471,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)],[170]) ).

thf(390,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/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).

thf(1993,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)],[390]) ).

thf(47,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( B
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).

thf(1162,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( B
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ( ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( C @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(919,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
        = ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).

thf(3192,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
        = ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).

thf(41,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(1149,plain,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(97,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).

thf(1293,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)],[97]) ).

thf(132,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).

thf(1381,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ 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)],[132]) ).

thf(900,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/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).

thf(3150,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)],[900]) ).

thf(28,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_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).

thf(1112,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_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(661,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/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(2605,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)],[661]) ).

thf(663,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__inf__iff_2) ).

thf(2610,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)],[663]) ).

thf(843,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__insert_0) ).

thf(3027,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( 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)],[843]) ).

thf(892,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/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

thf(3133,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)],[892]) ).

thf(209,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).

thf(1557,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(532,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__image ) ) ) )
      = ( C @ ( D @ ( D @ ( C @ ( C @ tc_fun ) @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Finite__Set_Ofold ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__image__def_0) ).

thf(2314,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__image ) ) ) )
      = ( C @ ( D @ ( D @ ( C @ ( C @ tc_fun ) @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Finite__Set_Ofold ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(448,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( A @ ( E @ c_in ) ) @ hBOOL )
      | ( ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__f__f_0) ).

thf(2129,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( A @ ( E @ c_in ) ) @ hBOOL )
      | ( ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(669,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( C @ ( E @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq12_0) ).

thf(2625,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( F @ ( C @ ( E @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(315,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).

thf(1821,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)],[315]) ).

thf(280,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).

thf(1731,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(592,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Diff__UNIV_0) ).

thf(2446,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(727,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/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(2757,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)],[727]) ).

thf(906,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).

thf(3165,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(331,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/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

thf(1862,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)],[331]) ).

thf(846,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I5_J_0) ).

thf(3034,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(110,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/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(1325,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)],[110]) ).

thf(656,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__left__idem_0) ).

thf(2593,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)],[656]) ).

thf(835,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( A @ ( E @ ( E @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( E @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__insert_0) ).

thf(3006,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( A @ ( E @ ( E @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( E @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(1029,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__absorb2_0) ).

thf(3451,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)],[1029]) ).

thf(635,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/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).

thf(2542,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)],[635]) ).

thf(678,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_Hoare__Mirabelle_Otriple @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( C @ ( C @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).

thf(2647,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ tc_Hoare__Mirabelle_Otriple @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( C @ ( C @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(707,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_Finite__Set_Ocard ) @ ( C @ ( B @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__seteq_0) ).

thf(2710,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_Finite__Set_Ocard ) @ ( C @ ( B @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(794,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/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).

thf(2911,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)],[794]) ).

thf(589,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).

thf(2439,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(548,axiom,
    ! [A: $i] :
      ( ( ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).

thf(2350,plain,
    ! [A: $i] :
      ( ( ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(467,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).

thf(2171,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(881,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ ( D @ ( A @ ( B @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 ) ) ) ) )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_1) ).

thf(3110,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ ( D @ ( A @ ( B @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 ) ) ) ) )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(520,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__inf__iff_1) ).

thf(2288,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)],[520]) ).

thf(971,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ~ ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).

thf(3310,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ~ ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(436,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( E @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( A @ ( E @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__permute__diff_0) ).

thf(2101,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( E @ ( D @ ( C @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( A @ ( E @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(264,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/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

thf(1694,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)],[264]) ).

thf(422,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

thf(2069,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(425,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/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).

thf(2075,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)],[425]) ).

thf(580,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(2418,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)],[580]) ).

thf(362,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).

thf(1926,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = C )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(555,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_in ) ) @ 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/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).

thf(2365,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_in ) ) @ 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)],[555]) ).

thf(266,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).

thf(1699,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(573,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
      | ( ( E @ ( A @ hAPP ) @ ( D @ ( C @ ( A @ ( B @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
        = E )
      | ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__f__eq_0) ).

thf(2401,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
      | ( ( E @ ( A @ hAPP ) @ ( D @ ( C @ ( A @ ( B @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
        = E )
      | ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(224,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/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).

thf(1594,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)],[224]) ).

thf(1018,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty_0) ).

thf(3423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(1,negated_conjecture,
    t_a @ ( v_F @ c_Finite__Set_Ofinite ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(1044,plain,
    t_a @ ( v_F @ c_Finite__Set_Ofinite ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(607,axiom,
    tc_bool @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(2481,plain,
    tc_bool @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(12,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C = E )
      | ( ( E @ ( 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 @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).

thf(1066,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C = E )
      | ( ( E @ ( 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 @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(159,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).

thf(1445,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(667,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( E @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq1_0) ).

thf(2620,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( E @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(500,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).

thf(2244,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( 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)],[500]) ).

thf(725,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).

thf(2752,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(125,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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

thf(1364,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)],[125]) ).

thf(568,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Ovimage ) ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_0) ).

thf(2390,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Ovimage ) ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(182,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/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

thf(1496,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)],[182]) ).

thf(527,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(2303,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(825,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I14_J_0) ).

thf(2984,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( 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)],[825]) ).

thf(309,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).

thf(1805,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(999,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/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).

thf(3380,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)],[999]) ).

thf(211,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).

thf(1562,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(1026,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

thf(3444,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(811,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(2952,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(439,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/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

thf(2107,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)],[439]) ).

thf(62,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( D @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != C )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).

thf(1203,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( D @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ( ( D @ ( C @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
       != C )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(686,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(2665,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)],[686]) ).

thf(830,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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_0) ).

thf(2994,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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(149,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).

thf(1420,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)],[149]) ).

thf(408,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_1) ).

thf(2037,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(260,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).

thf(1684,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(189,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).

thf(1509,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)],[189]) ).

thf(389,axiom,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
     != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).

thf(1990,plain,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
     != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(956,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Osetsum ) ) ) )
        = ( tc_nat @ ( B @ ( D @ ( A @ c_Finite__Set_Osetsum ) ) ) @ ( tc_nat @ ( B @ ( C @ ( A @ c_Finite__Set_Osetsum ) ) ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff__nat_0) ).

thf(3278,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_nat @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Finite__Set_Osetsum ) ) ) )
        = ( tc_nat @ ( B @ ( D @ ( A @ c_Finite__Set_Osetsum ) ) ) @ ( tc_nat @ ( B @ ( C @ ( A @ c_Finite__Set_Osetsum ) ) ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).

thf(962,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 )
      | ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
       != ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(3292,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 )
      | ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
       != ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).

thf(206,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).

thf(1551,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(4,negated_conjecture,
    t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( t_a @ ( v_F @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( t_a @ ( v_Q_H @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( t_a @ ( v_c0 @ ( t_a @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( v_P_H @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(1049,plain,
    t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( t_a @ ( v_F @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( t_a @ ( v_Q_H @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ ( t_a @ ( v_c0 @ ( t_a @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ tc_fun ) @ ( tc_Com_Ocom @ tc_fun ) @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( t_b @ tc_fun ) @ ( v_P_H @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ c_COMBB ) ) ) ) @ c_COMBS ) ) ) ) @ c_COMBS ) ) ) ) @ c_Set_Oimage ) ) ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(237,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/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(1626,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)],[237]) ).

thf(836,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/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

thf(3009,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)],[836]) ).

thf(845,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).

thf(3031,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( 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)],[845]) ).

thf(752,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) )
        = ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) @ ( A @ ( B @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__subset__Int_0) ).

thf(2816,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) )
        = ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) @ ( A @ ( B @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(251,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/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).

thf(1662,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)],[251]) ).

thf(665,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

thf(2614,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( 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)],[665]) ).

thf(102,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/sandbox/benchmark/theBenchmark.p',cls_le__maxI2_0) ).

thf(1304,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)],[102]) ).

thf(336,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/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(1873,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)],[336]) ).

thf(1020,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( B @ ( E @ ( A @ ( D @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).

thf(3427,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( B @ ( E @ ( A @ ( D @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(534,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 @ ( 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 ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__Un_0) ).

thf(2318,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 @ ( 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 ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(739,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

thf(2784,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)],[739]) ).

thf(924,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_1) ).

thf(3206,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)],[924]) ).

thf(91,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).

thf(1277,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(446,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(2124,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(495,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).

thf(2234,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(17,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).

thf(1081,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(801,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I6_J_0) ).

thf(2927,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(671,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/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

thf(2629,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)],[671]) ).

thf(39,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/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).

thf(1145,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)],[39]) ).

thf(766,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_0) ).

thf(2846,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)],[766]) ).

thf(505,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).

thf(2256,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(646,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/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).

thf(2567,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)],[646]) ).

thf(287,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

thf(1748,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)],[287]) ).

thf(1004,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/sandbox/benchmark/theBenchmark.p',cls_fold1__antimono_0) ).

thf(3391,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)],[1004]) ).

thf(709,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).

thf(2715,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(226,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/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).

thf(1598,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)],[226]) ).

thf(377,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).

thf(1961,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(571,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Ouminus )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Ouminus ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ouminus) ).

thf(2397,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Ouminus )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Ouminus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(684,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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(2661,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)],[684]) ).

thf(928,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/sandbox/benchmark/theBenchmark.p',cls_setsum__Un__disjoint_0) ).

thf(3214,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)],[928]) ).

thf(369,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).

thf(1941,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[369]) ).

thf(784,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__assoc_0) ).

thf(2888,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)],[784]) ).

thf(781,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

thf(2882,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(295,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).

thf(1770,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(997,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(3376,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)],[997]) ).

thf(821,axiom,
    tc_bool @ class_Orderings_Otop,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

thf(2977,plain,
    tc_bool @ class_Orderings_Otop,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(45,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).

thf(1156,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)],[45]) ).

thf(285,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).

thf(1743,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ 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)],[285]) ).

thf(140,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).

thf(1400,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(229,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).

thf(1605,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(948,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).

thf(3260,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).

thf(127,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/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

thf(1368,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)],[127]) ).

thf(934,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/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

thf(3228,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)],[934]) ).

thf(469,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).

thf(2175,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(299,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).

thf(1780,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(754,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( E @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).

thf(2821,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( E @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(289,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).

thf(1753,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)],[289]) ).

thf(566,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/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).

thf(2386,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)],[566]) ).

thf(72,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/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__left_0) ).

thf(1230,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)],[72]) ).

thf(176,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).

thf(1484,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)],[176]) ).

thf(462,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/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).

thf(2160,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)],[462]) ).

thf(723,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

thf(2747,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(647,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).

thf(2569,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(432,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(2092,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(303,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).

thf(1790,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(859,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(3063,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(56,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).

thf(1186,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)],[56]) ).

thf(985,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/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold1__Un_0) ).

thf(3344,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)],[985]) ).

thf(301,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/sandbox/benchmark/theBenchmark.p',cls_sup__max_0) ).

thf(1785,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)],[301]) ).

thf(585,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

thf(2429,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)],[585]) ).

thf(85,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

thf(1262,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(542,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).

thf(2337,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(350,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/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

thf(1901,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)],[350]) ).

thf(34,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).

thf(1130,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)],[34]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf_0) ).

thf(1738,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(114,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).

thf(1336,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ c_Suc @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(601,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( C @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).

thf(2468,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ ( B @ c_in ) ) @ 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)],[601]) ).

thf(550,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(2354,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(312,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).

thf(1813,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(162,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

thf(1452,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(981,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__negf_0) ).

thf(3334,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( D @ ( C @ ( A @ ( A @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ c_COMBB ) ) ) ) @ c_Finite__Set_Osetsum ) ) ) )
        = ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

thf(515,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).

thf(2276,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(385,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(1980,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(702,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 @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).

thf(2701,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 @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(610,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).

thf(2486,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(658,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).

thf(2599,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(790,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ 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_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

thf(2903,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ 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_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(258,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).

thf(1679,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( B @ ( C @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(1012,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/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

thf(3412,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)],[1012]) ).

thf(616,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(2500,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(202,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( B @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).

thf(1543,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( C @ ( B @ ( E @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[202]) ).

thf(348,axiom,
    tc_nat @ class_HOL_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

thf(1898,plain,
    tc_nat @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(642,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/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

thf(2558,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)],[642]) ).

thf(989,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) @ hBOOL )
      | ~ ( F @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__into_0) ).

thf(3356,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) @ hBOOL )
      | ~ ( F @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).

thf(932,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

thf(3224,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).

thf(186,axiom,
    ! [A: $i] : ( A @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).

thf(1504,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)],[186]) ).

thf(340,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/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(1881,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)],[340]) ).

thf(767,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__iff__inf_1) ).

thf(2848,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)],[767]) ).

thf(510,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).

thf(2266,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ 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)],[510]) ).

thf(960,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infI_0) ).

thf(3288,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)],[960]) ).

thf(142,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).

thf(1404,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)],[142]) ).

thf(123,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).

thf(1358,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)],[123]) ).

thf(888,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/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

thf(3124,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)],[888]) ).

thf(828,axiom,
    ! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(2992,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(267,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

thf(1702,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)],[267]) ).

thf(563,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).

thf(2379,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).

thf(1284,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(820,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/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).

thf(2975,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)],[820]) ).

thf(121,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).

thf(1353,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)],[121]) ).

thf(516,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/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).

thf(2279,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)],[516]) ).

thf(455,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_3) ).

thf(2145,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)],[455]) ).

thf(220,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/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

thf(1585,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)],[220]) ).

thf(22,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

thf(1094,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)],[22]) ).

thf(772,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_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).

thf(2860,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_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(712,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).

thf(2722,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(76,axiom,
    ! [B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).

thf(1240,plain,
    ! [B: $i,A: $i] :
      ( c_Com_Ocom_OSKIP
     != ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(233,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(1617,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(958,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(3284,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).

thf(398,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

thf(2013,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(606,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/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).

thf(2479,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)],[606]) ).

thf(1008,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).

thf(3401,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)],[1008]) ).

thf(54,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).

thf(1180,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)],[54]) ).

thf(379,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

thf(1966,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(909,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/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(3171,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)],[909]) ).

thf(1027,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).

thf(3447,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).

thf(917,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).

thf(3188,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( 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)],[917]) ).

thf(537,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_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).

thf(2325,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_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(484,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/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).

thf(2209,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)],[484]) ).

thf(683,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
       != ( G @ ( F @ ( E @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).

thf(2658,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
       != ( G @ ( F @ ( E @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(848,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).

thf(3039,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( A @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(392,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/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

thf(1998,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)],[392]) ).

thf(774,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ 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_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff_0) ).

thf(2865,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ 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_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(778,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/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(2875,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)],[778]) ).

thf(107,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/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

thf(1316,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)],[107]) ).

thf(246,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( C @ ( B @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).

thf(1649,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( C @ ( B @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[246]) ).

thf(18,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_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( 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_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).

thf(1084,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_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = ( C @ ( B @ ( 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_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(165,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/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

thf(1459,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)],[165]) ).

thf(411,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/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(2045,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)],[411]) ).

thf(873,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__transfer_0) ).

thf(3092,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 ) ) ) @ c_in ) ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(700,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/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(2696,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)],[700]) ).

thf(207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).

thf(1553,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( B @ ( C @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(776,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/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(2870,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)],[776]) ).

thf(758,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(2828,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(426,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(2078,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(320,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).

thf(1834,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)],[320]) ).

thf(530,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).

thf(2310,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(324,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ c_Suc @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).

thf(1844,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ 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)],[324]) ).

thf(248,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/sandbox/benchmark/theBenchmark.p',cls_Max__def__raw_0) ).

thf(1654,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)],[248]) ).

thf(145,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

thf(1412,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)],[145]) ).

thf(487,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I15_J_0) ).

thf(2215,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( 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)],[487]) ).

thf(192,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).

thf(1517,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(612,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).

thf(2490,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(57,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

thf(1189,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(136,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/sandbox/benchmark/theBenchmark.p',cls_le__maxI1_0) ).

thf(1390,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)],[136]) ).

thf(797,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(2919,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(217,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).

thf(1575,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(856,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff__eq__card_0) ).

thf(3056,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(163,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/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

thf(1453,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)],[163]) ).

thf(281,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

thf(1734,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)],[281]) ).

thf(792,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/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).

thf(2907,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)],[792]) ).

thf(705,axiom,
    ! [A: $i] : ( A @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).

thf(2707,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(275,axiom,
    tc_nat @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

thf(1721,plain,
    tc_nat @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(514,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
       != ( G @ ( F @ ( E @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).

thf(2273,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = G )
      | ( ( D @ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
       != ( G @ ( F @ ( E @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(640,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(2554,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(630,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).

thf(2532,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(175,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
       != ( B @ ( C @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).

thf(1481,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
       != ( B @ ( C @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(755,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/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).

thf(2823,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)],[755]) ).

thf(403,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 ) ) @ c_in ) ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__eqI_0) ).

thf(2026,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 ) ) @ c_in ) ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(328,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).

thf(1854,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)],[328]) ).

thf(662,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).

thf(2608,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(730,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__greatest_0) ).

thf(2764,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)],[730]) ).

thf(195,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/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).

thf(1523,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)],[195]) ).

thf(945,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).

thf(3252,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(245,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).

thf(1646,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)],[245]) ).

thf(591,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I22_J_0) ).

thf(2443,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(518,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_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Int_0) ).

thf(2283,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_HOL_Ouminus__class_Ouminus @ hAPP ) )
      = ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(172,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/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

thf(1476,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)],[172]) ).

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/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).

thf(1341,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(1042,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

thf(3484,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).

thf(770,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( B = C )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).

thf(2855,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( B = C )
      | ~ ( E @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(242,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/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(1639,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)],[242]) ).

thf(521,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/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

thf(2290,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)],[521]) ).

thf(503,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__inf__iff_0) ).

thf(2251,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)],[503]) ).

thf(351,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

thf(1903,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(575,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/sandbox/benchmark/theBenchmark.p',cls_setsum__Un__Int_0) ).

thf(2406,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)],[575]) ).

thf(750,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).

thf(2811,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(238,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).

thf(1629,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( B @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( C @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(979,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).

thf(3331,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(893,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ 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_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).

thf(3136,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ 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_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(994,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).

thf(3368,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).

thf(459,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( D @ ( G @ c_Finite__Set_Ofinite ) )
      | ( D @ ( G @ ( F @ c_in ) ) @ hBOOL )
      | ( ( D @ ( G @ ( F @ c_Set_Oinsert ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__image ) ) ) @ hAPP ) @ hAPP ) )
        = ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__image ) ) ) @ hAPP ) @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__image__insert_0) ).

thf(2152,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_OrderedGroup_Oab__semigroup__mult ) )
      | ~ ( D @ ( G @ c_Finite__Set_Ofinite ) )
      | ( D @ ( G @ ( F @ c_in ) ) @ hBOOL )
      | ( ( D @ ( G @ ( F @ c_Set_Oinsert ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__image ) ) ) @ hAPP ) @ hAPP ) )
        = ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__image ) ) ) @ hAPP ) @ hAPP ) @ ( F @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(508,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(2262,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)],[508]) ).

thf(813,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).

thf(2956,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)],[813]) ).

thf(744,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(2796,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)],[744]) ).

thf(572,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).

thf(2399,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(157,axiom,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

thf(1440,plain,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(479,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 )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__eqI_1) ).

thf(2198,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 )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ c_Finite__Set_Olinorder__class_OMax @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(269,axiom,
    tc_nat @ class_HOL_Ominus,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).

thf(1706,plain,
    tc_nat @ class_HOL_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(463,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/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

thf(2162,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)],[463]) ).

thf(230,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).

thf(1607,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)],[230]) ).

thf(444,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).

thf(2120,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ~ ( B @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(433,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).

thf(2095,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)],[433]) ).

thf(719,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/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(2739,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)],[719]) ).

thf(6,negated_conjecture,
    ! [A: $i] :
      ( ~ ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_Q_H @ hAPP ) @ ( A @ ( v_c0 @ hAPP ) @ ( A @ ( v_P_H @ hAPP ) @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_Q @ hAPP ) @ ( A @ ( v_c0 @ hAPP ) @ ( A @ ( v_P @ hAPP ) @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

thf(1045,plain,
    ! [A: $i] :
      ( ~ ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_Q_H @ hAPP ) @ ( A @ ( v_c0 @ hAPP ) @ ( A @ ( v_P_H @ hAPP ) @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
      | ( t_b @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_b @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( v_Q @ hAPP ) @ ( A @ ( v_c0 @ hAPP ) @ ( A @ ( v_P @ hAPP ) @ ( t_b @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( v_G @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(914,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/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

thf(3181,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)],[914]) ).

thf(565,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( E @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq1_1) ).

thf(2384,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( E @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(604,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/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

thf(2475,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)],[604]) ).

thf(740,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 )
      | ~ ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__fold1__iff_0) ).

thf(2786,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 )
      | ~ ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(473,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

thf(2183,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(65,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).

thf(1212,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)],[65]) ).

thf(493,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( F @ ( G @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ( D
        = ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( D @ ( E @ ( F @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Obelow__fold1__iff_0) ).

thf(2230,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( F @ ( G @ ( A @ c_Lattices_Olower__semilattice ) ) ) )
      | ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ( D
        = ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( D @ ( E @ ( F @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(104,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(1309,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)],[104]) ).

thf(737,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/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).

thf(2779,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)],[737]) ).

thf(400,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/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).

thf(2019,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)],[400]) ).

thf(1016,axiom,
    tc_bool @ class_Lattices_Oboolean__algebra,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).

thf(3420,plain,
    tc_bool @ class_Lattices_Oboolean__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(232,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

thf(1614,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(581,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).

thf(2421,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(560,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).

thf(2374,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(711,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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ofold1__Un_0) ).

thf(2719,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)],[711]) ).

thf(23,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).

thf(1097,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)],[23]) ).

thf(494,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).

thf(2233,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(877,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

thf(3100,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(223,axiom,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

thf(1593,plain,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(982,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oinsert ) ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

thf(3337,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_in ) ) @ hBOOL )
      | ( ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oinsert ) ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).

thf(923,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).

thf(3203,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).

thf(1036,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/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).

thf(3469,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)],[1036]) ).

thf(354,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/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

thf(1908,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)],[354]) ).

thf(394,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_fold1__insert__idem_0) ).

thf(2003,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( 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)],[394]) ).

thf(454,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A @ ( B @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).

thf(2142,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A @ ( B @ ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) @ c_in ) ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(802,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

thf(2930,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(488,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(2218,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)],[488]) ).

thf(506,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/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(2258,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)],[506]) ).

thf(35,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).

thf(1133,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(623,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/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

thf(2517,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)],[623]) ).

thf(694,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__le1_0) ).

thf(2683,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)],[694]) ).

thf(460,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A
        = ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 ) ) ) @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_range__ex1__eq_0) ).

thf(2155,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A
        = ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 ) ) ) @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(631,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( A @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( A @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).

thf(2534,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( A @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( E @ ( 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)],[631]) ).

thf(936,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).

thf(3232,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) @ hBOOL )
      | ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).

thf(717,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).

thf(2736,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(396,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ ( G @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).

thf(2008,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( t_a @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ ( G @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( 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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(79,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/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).

thf(1248,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)],[79]) ).

thf(413,axiom,
    ( ( v_R @ ( t_c @ ( t_b @ ( t_a @ ( v_Q @ ( v_P @ c_COMBS ) ) ) ) @ hAPP ) )
    = ( v_R @ ( v_Q @ hAPP ) @ ( v_R @ ( v_P @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def__raw_0) ).

thf(2050,plain,
    ( ( v_R @ ( t_c @ ( t_b @ ( t_a @ ( v_Q @ ( v_P @ c_COMBS ) ) ) ) @ hAPP ) )
    = ( v_R @ ( v_Q @ hAPP ) @ ( v_R @ ( v_P @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(978,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

thf(3328,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) @ hBOOL )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(480,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(2201,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)],[480]) ).

thf(313,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/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

thf(1816,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)],[313]) ).

thf(423,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/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).

thf(2070,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)],[423]) ).

thf(704,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( D @ ( E @ c_in ) ) @ hBOOL )
      | ( ( A @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( E @ ( B @ hAPP ) @ ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__ring_0) ).

thf(2704,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( D @ ( E @ c_in ) ) @ hBOOL )
      | ( ( A @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Finite__Set_Osetsum ) ) ) )
        = ( E @ ( B @ hAPP ) @ ( A @ ( C @ ( D @ ( B @ c_Finite__Set_Osetsum ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(844,axiom,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(3030,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(409,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( F @ ( B @ c_in ) ) @ hBOOL )
      | ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
        = ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).

thf(2040,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( F @ ( B @ c_in ) ) @ hBOOL )
      | ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
        = ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(48,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/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(1165,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)],[48]) ).

thf(851,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/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).

thf(3045,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)],[851]) ).

thf(680,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).

thf(2651,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

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

thf(2549,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)],[638]) ).

thf(970,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(3309,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(898,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/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

thf(3145,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)],[898]) ).

thf(155,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).

thf(1436,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)],[155]) ).

thf(330,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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

thf(1859,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)],[330]) ).

thf(249,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).

thf(1657,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(541,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).

thf(2334,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(986,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert_0) ).

thf(3347,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ c_Finite__Set_Ocard ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).

thf(955,axiom,
    tc_bool @ class_Lattices_Oupper__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(3277,plain,
    tc_bool @ class_Lattices_Oupper__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).

thf(51,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/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

thf(1172,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)],[51]) ).

thf(1040,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__diff_0) ).

thf(3479,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).

thf(144,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 @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).

thf(1410,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 @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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)],[144]) ).

thf(815,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/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty_0) ).

thf(2961,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)],[815]) ).

thf(271,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/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

thf(1710,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)],[271]) ).

thf(59,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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

thf(1197,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)],[59]) ).

thf(795,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( B @ ( A @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Ofold1__eq__fold__idem_0) ).

thf(2913,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_OrderedGroup_Oab__semigroup__idem__mult ) )
      | ~ ( B @ ( D @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( D @ ( C @ ( B @ ( B @ ( A @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(574,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/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).

thf(2404,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)],[574]) ).

thf(976,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( B @ ( A @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__eq__fold_0) ).

thf(3323,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
      | ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( C @ ( B @ ( A @ ( A @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).

thf(1019,axiom,
    tc_bool @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(3426,plain,
    tc_bool @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(345,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

thf(1891,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)],[345]) ).

thf(490,axiom,
    ( ( v_R @ ( v_Q @ ( t_c @ ( t_b @ ( t_a @ ( v_P @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
    = ( v_Q @ ( v_R @ ( v_P @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def__raw_0) ).

thf(2223,plain,
    ( ( v_R @ ( v_Q @ ( t_c @ ( t_b @ ( t_a @ ( v_P @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
    = ( v_Q @ ( v_R @ ( v_P @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(171,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__compl__top_0) ).

thf(1473,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(401,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(2021,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(419,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).

thf(2063,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(549,axiom,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

thf(2353,plain,
    ! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(992,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/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

thf(3362,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)],[992]) ).

thf(842,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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).

thf(3025,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 @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( C @ ( B @ ( t_a @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ c_Set_Oinsert ) ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).

thf(1152,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ ( C @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( tc_nat @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_nat @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(747,axiom,
    ! [B: $i,A: $i] :
      ( ( ( v_x @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ hAPP ) )
        = ( v_x @ ( B @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_HOL_Ouminus ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).

thf(2803,plain,
    ! [B: $i,A: $i] :
      ( ( ( v_x @ ( B @ ( A @ ( t_a @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ hAPP ) )
        = ( v_x @ ( B @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) )
      | ~ ( A @ class_HOL_Ouminus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(991,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(3360,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).

thf(383,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_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).

thf(1976,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_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(652,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( F @ c_Finite__Set_Ofinite ) )
      | ( C @ ( F @ ( E @ c_in ) ) @ hBOOL )
      | ( ( C @ ( F @ ( E @ c_Set_Oinsert ) ) @ ( D @ ( C @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__image ) ) ) @ hAPP ) @ hAPP ) )
        = ( F @ ( D @ ( C @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__image ) ) ) @ hAPP ) @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__image__insert_0) ).

thf(2583,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( F @ c_Finite__Set_Ofinite ) )
      | ( C @ ( F @ ( E @ c_in ) ) @ hBOOL )
      | ( ( C @ ( F @ ( E @ c_Set_Oinsert ) ) @ ( D @ ( C @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__image ) ) ) @ hAPP ) @ hAPP ) )
        = ( F @ ( D @ ( C @ ( A @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ c_Finite__Set_Ofold__image ) ) ) @ hAPP ) @ hAPP ) @ ( 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)],[652]) ).

thf(619,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(2507,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(100,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ c_Orderings_Oord__class_Omax @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).

thf(1299,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)],[100]) ).

thf(701,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/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

thf(2699,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)],[701]) ).

thf(559,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/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

thf(2372,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)],[559]) ).

thf(452,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).

thf(2138,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(74,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/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(1236,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)],[74]) ).

thf(617,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = 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/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

thf(2502,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = 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)],[617]) ).

thf(890,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_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).

thf(3128,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_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(318,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

thf(1829,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(817,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/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).

thf(2966,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)],[817]) ).

thf(88,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(1268,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)],[88]) ).

thf(788,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

thf(2898,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
        = ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(133,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/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

thf(1384,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)],[133]) ).

thf(199,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/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).

thf(1537,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)],[199]) ).

thf(184,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup_0) ).

thf(1500,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(942,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBS ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def_0) ).

thf(3245,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBS ) ) ) ) @ hAPP ) )
      = ( F @ ( B @ hAPP ) @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).

thf(840,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 )
      | ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
       != ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).

thf(3020,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 )
      | ( ( C @ ( B @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
       != ( E @ ( D @ ( A @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).

thf(633,axiom,
    tc_bool @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(2539,plain,
    tc_bool @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(272,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).

thf(1713,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ c_Suc @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(696,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( B @ hAPP ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__f__f_0) ).

thf(2687,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( B @ hAPP ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Fun_Othe__inv__into ) ) ) @ hAPP ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(339,axiom,
    tc_nat @ class_Lattices_Olower__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).

thf(1880,plain,
    tc_nat @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(153,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/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(1431,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)],[153]) ).

thf(865,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( A @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_sup__le__fold__sup_0) ).

thf(3076,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( A @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) @ ( 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)],[865]) ).

thf(882,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/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(3113,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)],[882]) ).

thf(1005,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( A @ ( C @ ( D @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( A @ ( C @ ( E @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( A @ ( C @ ( D @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( 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/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).

thf(3394,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( A @ ( C @ ( D @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( A @ ( C @ ( E @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( A @ ( C @ ( D @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( 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)],[1005]) ).

thf(187,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/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(1505,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)],[187]) ).

thf(512,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).

thf(2270,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(235,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/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).

thf(1621,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)],[235]) ).

thf(726,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 ) ) @ c_in ) ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__eqI_0) ).

thf(2754,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 ) ) @ c_in ) ) @ hBOOL )
      | ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ( ( B @ ( A @ c_Finite__Set_Olinorder__class_OMin @ hAPP ) )
        = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(1033,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__image ) ) ) @ hAPP ) @ hAPP ) )
      = E ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__image__empty_0) ).

thf(3461,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__image ) ) ) @ hAPP ) @ hAPP ) )
      = E ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).

thf(535,axiom,
    ( ( v_Q @ ( t_b @ ( t_a @ ( v_P @ c_COMBK ) ) @ hAPP ) )
    = v_P ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def__raw_0) ).

thf(2321,plain,
    ( ( v_Q @ ( t_b @ ( t_a @ ( v_P @ c_COMBK ) ) @ hAPP ) )
    = v_P ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(644,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/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

thf(2563,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)],[644]) ).

thf(760,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(2832,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(147,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).

thf(1416,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)],[147]) ).

thf(1022,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 ) )
      | ( ( B @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) )
        = ( D @ ( B @ ( A @ c_Finite__Set_Ofold1 ) @ hAPP ) @ ( C @ ( A @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Ofold1__insert__idem_0) ).

thf(3432,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 ) )
      | ( ( B @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( 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)],[1022]) ).

thf(430,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/sandbox/benchmark/theBenchmark.p',cls_Max__mono_0) ).

thf(2087,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)],[430]) ).

thf(13,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

thf(1069,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)],[13]) ).

thf(682,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__iff__inf_0) ).

thf(2655,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)],[682]) ).

thf(112,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/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).

thf(1331,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)],[112]) ).

thf(1038,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I20_J_0) ).

thf(3474,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
        = ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).

thf(689,axiom,
    tc_bool @ class_Lattices_Olower__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

thf(2672,plain,
    tc_bool @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(675,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Otop )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).

thf(2640,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Otop )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(371,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/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).

thf(1945,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)],[371]) ).

thf(927,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).

thf(3212,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).

thf(965,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/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(3299,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)],[965]) ).

thf(875,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/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).

thf(3096,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)],[875]) ).

thf(482,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__the__inv__into_0) ).

thf(2206,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(697,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 @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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 )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).

thf(2690,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 @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) @ ( 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 )
      | ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(832,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( 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 ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).

thf(2998,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( 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 ) )
       != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(497,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 @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__mono_0) ).

thf(2238,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 @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(179,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

thf(1490,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)],[179]) ).

thf(524,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/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Ole__infE_1) ).

thf(2297,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)],[524]) ).

thf(595,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

thf(2453,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ominus__class_Ominus @ hAPP ) @ hAPP ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(854,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

thf(3052,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( F @ ( E @ ( B @ c_in ) ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(973,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( G @ ( E @ ( F @ ( D @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( G @ ( E @ ( F @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).

thf(3316,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
      | ~ ( G @ ( E @ ( F @ ( D @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
      | ( G @ ( E @ ( F @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).

thf(761,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).

thf(2834,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(20,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C = E )
      | ( ( E @ ( 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 @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).

thf(1088,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C = E )
      | ( ( E @ ( 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 @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( A @ c_HOL_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(829,axiom,
    ! [A: $i] : ( A @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).

thf(2993,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = C )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__unique_0) ).

thf(1449,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
        = C )
      | ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Obot__class_Obot ) )
      | ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
       != ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(169,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

thf(1468,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)],[169]) ).

thf(852,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/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).

thf(3047,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)],[852]) ).

thf(602,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).

thf(2470,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ~ ( B @ ( C @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ ( tc_nat @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(356,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/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

thf(1912,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)],[356]) ).

thf(823,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(2980,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(3554,plain,
    $false,
    inference(e,[status(thm)],[2163,1322,1718,2612,2744,1767,1729,3167,2412,1840,1850,2427,3449,2544,2331,2295,2306,2341,2109,2031,3399,1995,2921,3477,2463,3397,1899,1818,1295,1956,1950,1549,2363,3185,2512,1290,2622,2395,1618,3153,2590,3098,2676,3108,3012,3382,1486,3072,1924,2117,2940,1596,2808,1522,3230,2381,1443,2776,1808,2947,1569,1939,2099,1591,2837,1142,1971,1793,3017,3049,1756,3365,3175,2316,2448,2434,1233,2580,1078,1788,1426,3217,3120,3429,3004,2035,2627,2168,1260,1919,1988,3414,1761,2901,3313,1063,2844,1507,1222,2972,2886,1746,3103,2348,3350,2432,1914,1243,1127,1782,3088,1046,3308,2010,1935,3281,3466,3140,1724,2173,1366,1529,2067,2825,2819,1803,2136,1904,1623,1254,3195,1660,2339,3342,1871,3061,2708,3148,1511,1826,1832,3353,2126,3043,2703,3263,1287,3221,2603,2328,2916,2814,1985,3116,2667,1313,1279,2185,1577,3089,2488,2745,2571,2356,1545,1922,2713,1147,1479,1115,1931,2158,1641,1773,2852,2388,1100,3268,1847,3374,3385,3463,1379,1087,1514,1319,1704,1890,1347,1572,1741,3084,3014,2730,2301,1494,2989,1963,1875,1778,2178,2090,1109,3163,3290,2777,1489,2950,1415,1302,1664,2105,3075,1373,2996,1911,3295,2782,1418,2451,2236,2880,1682,1136,3438,1864,2122,2925,1978,1677,2540,1183,2073,2058,2281,1886,1526,1433,2103,1600,1697,3406,1564,3378,3389,2964,2367,2437,1896,2190,3421,1447,2483,1072,2530,2523,1796,1394,2772,2242,1345,3226,1943,1201,3184,2586,2884,3435,2954,2922,1206,1691,1306,1199,1338,3418,2574,1438,3169,3265,2047,3318,1311,3054,2083,1736,2496,2905,1868,2061,1636,1047,3037,1057,2589,1387,1091,2601,2249,2596,1255,1751,1666,2969,2528,1274,2673,2264,2409,2733,1343,2560,1355,1580,1217,2147,3239,3069,3371,2937,1824,2150,1370,2132,2414,3250,3286,1560,2873,1837,2670,2477,3297,1178,1888,1687,1159,2181,2112,1573,2769,2958,1423,3403,1968,2565,3198,2663,1555,2826,2327,2213,2211,1407,2547,2344,1281,2741,1634,1392,2228,2653,1106,1402,1350,1983,2115,3122,1121,2577,1227,2694,1672,3119,3078,3237,1118,2268,3001,2498,1541,3482,2515,3254,2377,2801,1534,1953,2685,2841,1328,2692,1498,1878,2631,2724,2858,3176,1397,1567,3143,1361,3210,2830,2868,1075,2080,1937,1810,1214,1644,2460,1493,2798,3141,2877,2023,3326,2323,3179,3094,1461,3441,2312,2455,2053,2196,2240,1842,2551,2085,1612,2649,2978,2472,3242,2285,3059,1266,1974,2851,2505,2006,1799,1947,1852,3074,2272,2140,2370,1776,1263,2932,1588,1150,1478,2519,2536,1297,3126,2681,1539,1456,2465,1060,1429,3247,3409,2862,2766,2052,2482,1246,1715,3333,3083,3201,1759,3454,1333,2203,2761,2208,2043,3173,1170,1466,1167,2645,2617,2423,2909,2634,2749,1857,3306,1054,3321,2368,2793,3190,1906,2001,1727,2176,2292,3042,1548,3274,2894,2376,1631,1251,1764,3130,1959,2556,1103,3358,2253,2033,2149,3257,2717,1219,3158,2260,1154,3387,2727,1916,3234,2789,2525,3472,2016,2806,3458,1520,1124,2134,2225,1884,2791,3240,2188,2981,2393,3086,1652,3081,1929,1388,3272,2029,1707,2738,2935,2055,2166,2457,1258,3304,1464,3302,1224,2358,1675,1139,1503,2193,3023,1669,3118,2220,2891,1271,2308,3208,1865,3340,1239,2442,2759,2425,3416,2510,2361,2521,1209,2679,2637,2774,1048,1933,3106,1722,2839,3138,1376,3160,1194,2346,2642,3155,2415,2987,1894,2493,2097,3270,2246,1603,2299,2943,2945,1043,1801,1690,3066,2896,2065,1175,3456,3219,1471,1993,1162,3192,1149,1293,1381,3150,1112,2605,2610,3027,3133,1557,2314,2129,2625,1821,1731,2446,2757,3165,1862,3034,1325,2593,3006,3451,2542,2647,2710,2911,2439,2350,2171,3110,2288,3310,2101,1694,2069,2075,2418,1926,2365,1699,2401,1594,3423,1044,2481,1066,1445,2620,2244,2752,1364,2390,1496,2303,2984,1805,3380,1562,3444,2952,2107,1203,2665,2994,1420,2037,1684,1509,1990,3278,3292,1551,1049,1626,3009,3031,2816,1662,2614,1304,1873,3427,2318,2784,3206,1277,2124,2234,1081,2927,2629,1145,2846,2256,2567,1748,3391,2715,1598,1961,2397,2661,3214,1941,2888,2882,1770,3376,2977,1156,1743,1400,1605,3260,1368,3228,2175,1780,2821,1753,2386,1230,1484,2160,2747,2569,2092,1790,3063,1186,3344,1785,2429,1262,2337,1901,1130,1738,1336,2468,2354,1813,1452,3334,2276,1980,2701,2486,2599,2903,1679,3412,2500,1543,1898,2558,3356,3224,1504,1881,2848,2266,3288,1404,1358,3124,2992,1702,2379,1284,2975,1353,2279,2145,1585,1094,2860,2722,1240,1617,3284,2013,2479,3401,1180,1966,3171,3447,3188,2325,2209,2658,3039,1998,2865,2875,1316,1649,1084,1459,2045,3092,2696,1553,2870,2828,2078,1834,2310,1844,1654,1412,2215,1517,2490,1189,1390,2919,1575,3056,1453,1734,2907,2707,1721,2273,2554,2532,1481,2823,2026,1854,2608,2764,1523,3252,1646,2443,2283,1476,1341,3484,2855,1639,2290,2251,1903,2406,2811,1629,3331,3136,3368,2152,2262,2956,2796,2399,1440,2198,1706,2162,1607,2120,2095,2739,1045,3181,2384,2475,2786,2183,1212,2230,1309,2779,2019,3420,1614,2421,2374,2719,1097,2233,3100,1593,3337,3203,3469,1908,2003,2142,2930,2218,2258,1133,2517,2683,2155,2534,3232,2736,2008,1248,2050,3328,2201,1816,2070,2704,3030,2040,1165,3045,2651,2549,3309,3145,1436,1859,1657,2334,3347,3277,1172,3479,1410,2961,1710,1197,2913,2404,3323,3426,1891,2223,1473,2021,2063,2353,3362,3025,1152,2803,3360,1976,2583,2507,1299,2699,2372,2138,1236,2502,3128,1829,2966,1268,2898,1384,1537,1500,3245,3020,2539,1713,2687,1880,1431,3076,3113,3394,1505,2270,1621,2754,3461,2321,2563,2832,1416,3432,2087,1069,2655,1331,3474,2672,2640,1945,3212,3299,3096,2206,2690,2998,2238,1490,2297,2453,3052,3316,2834,1088,2993,1449,1468,3047,2470,1912,2980]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SWV844-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.38  % Computer : n007.cluster.edu
% 0.10/0.38  % Model    : x86_64 x86_64
% 0.10/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38  % Memory   : 8046.5625MB
% 0.10/0.38  % OS       : Linux 6.8.0-71-generic
% 0.10/0.38  % CPULimit : 300
% 0.10/0.38  % WCLimit  : 300
% 0.10/0.38  % DateTime : Sat Sep 26 15:00:54 UTC 2026
% 0.10/0.38  % CPUTime  : 
% 0.10/0.38  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.72/0.70  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.41/1.01  % [INFO] 	 Parsing done (305ms). 
% 1.41/1.02  % [INFO] 	 Running in sequential loop mode. 
% 2.83/1.37  % [INFO] 	 eprover registered as external prover. 
% 2.83/1.38  % [INFO] 	 Scanning for conjecture ... 
% 4.19/1.92  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1035 axioms. Running axiom selection ... 
% 5.46/2.49  % [INFO] 	 Axiom selection finished. Selected 1035 axioms (removed 0 axioms). 
% 7.10/3.12  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 7.39/3.18  % [INFO] 	 Type checking passed. 
% 7.39/3.19  % [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 ... 
% 25.17/10.04  % External prover 'e' found a proof!
% 25.17/10.04  % [INFO] 	 Killing All external provers ... 
% 25.17/10.04  % Time passed: 9552ms (effective reasoning time: 9020ms)
% 25.38/10.05  % Axioms used in derivation (1035): cls_inf__sup__aci_I2_J_0, cls_ab__semigroup__mult_Omult__left__commute_0, cls_atLeastatMost__subset__iff_2, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_add__cancel__end_1, cls_subset__insert_1, cls_Diff__iff_2, cls_Min__insert_0, cls_Compl__subset__Compl__iff_1, cls_bot__fun__eq_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_inj__image__mem__iff_1, cls_top__fun__eq_0, cls_atLeastatMost__psubset__iff_1, cls_inf__sup__absorb_0, clsarity_nat__HOL_Oord, cls_vimage__code_0, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_setsum__diff__nat_0, cls_Diff__cancel_0, cls_min__max_Oinf__commute_0, cls_Int__absorb2_0, cls_minus__le__iff_0, cls_Diff1__fold__graph_0, cls_min__max_Ole__infE_0, cls_eq__add__iff2_1, cls_order__le__less__trans_0, cls_min__max_Oless__infI1_0, cls_sup__max_0, cls_less__diff__iff_1, cls_image__constant_0, cls_Compl__Diff__eq_0, cls_compl__sup_0, cls_Un__Diff_0, cls_com_Osimps_I3_J_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_comm__semiring__class_Odistrib_0, cls_Suc__mono_0, cls_min__add__distrib__left_0, cls_equalityI_0, cls_le__diff__iff_0, cls_insert__inter__insert_0, cls_lower__semilattice_Oinf__left__idem_0, cls_min__max_Osup__inf__distrib1_0, cls_Nat_Odiff__diff__eq_0, cls_sup__ge1_0, cls_ivl__disj__un_I21_J_0, cls_add__less__cancel__left_1, cls_insertE_0, cls_Inf__fold__inf_0, cls_less__fun__def_1, cls_Un__subset__iff_0, cls_Suc__inject_0, cls_ivl__disj__un_I20_J_0, cls_eq__imp__le_0, cls_sup__top__left_0, cls_inj__on__iff__eq__card_0, cls_inj__on__Un_2, cls_setsum__diff_0, cls_COMBC__def_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_range__ex1__eq_0, cls_min__max_Oinf__sup__distrib1_0, cls_the__inv__f__f_0, cls_empty__is__image_1, cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0, cls_image__mono_0, cls_Un__empty__left_0, cls_termination__basic__simps_I5_J_0, cls_le__funD_0, cls_atLeastatMost__psubset__iff_2, cls_fun__upd__image_1, cls_xt1_I12_J_0, cls_ab__semigroup__mult_Ofold1__Un_0, cls_finite__insert_0, cls_Diff__eq_0, cls_Suc__n__not__n_0, cls_min__max_Ole__sup__iff_2, cls_inj__on__image__Int_0, cls_fold1__eq__fold__idem_0, cls_min__max_Oinf__le1_0, cls_square__eq__iff_1, cls_inj__image__eq__iff_0, cls_min__less__iff__conj_0, cls_range__ex1__eq_3, cls_sup__bot__right_0, cls_fold1__insert_0, cls_insert__code_1, cls_fun__upd__apply_1, clsarity_nat__Lattices_Odistrib__lattice, cls_atLeastLessThan__subset__iff_1, cls_Int__atLeastAtMost_0, clsarity_bool__Lattices_Olower__semilattice, cls_finite__vimageI_0, cls_less__antisym_0, cls_inf__sup__aci_I6_J_0, cls_Un__upper1_0, cls_Un__commute_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_image__Int_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_eq__diff__iff_0, cls_card__insert_0, cls_dual__semilattice_0, cls_setsum__Un_0, cls_distrib__sup__le_0, cls_Int__mono_0, cls_linorder__neqE_0, cls_add__strict__right__mono_0, cls_Min__eqI_1, cls_vimage__Diff_0, cls_add__sup__distrib__right_0, cls_le__iff__inf_1, cls_conseq_0, cls_lower__semilattice_Oab__semigroup__idem__mult__inf_0, cls_lower__semilattice_Ole__inf__iff_0, cls_fun__Compl__def_0, cls_lower__semilattice_Oinf__commute_0, clsarity_fun__Orderings_Oorder, cls_finite__Un_2, cls_COMBK__def_0, cls_min__max_Osup__inf__absorb_0, cls_UnCI_1, cls_ivl__disj__un_I22_J_0, cls_minus__add__distrib_0, cls_add__le__cancel__left_1, cls_Int__insert__left_0, cls_triple_Oinject_1, cls_ab__semigroup__idem__mult__inf_0, cls_add__imp__eq_0, cls_min__less__iff__disj_2, cls_the__inv__into__onto_0, cls_mem__def_1, cls_add__le__cancel__right_1, cls_fun__upd__image_0, clsarity_nat__Orderings_Olinorder, cls_Diff__Un_0, cls_setsum__Un__disjoint_0, cls_ab__semigroup__mult_Omult__ac_I1_J_0, cls_Inf__lower_0, cls_insert__absorb_0, cls_empty__iff_0, cls_Min__le_0, cls_sup__le__fold__sup_0, cls_setsum__Un__Int_0, cls_Suc__lessI_0, cls_Int__subset__iff_2, cls_less__Suc__eq_2, cls_atLeastatMost__psubset__iff_3, cls_le__inf__iff_1, cls_fold__graph__imp__finite_0, clsarity_bool__HOL_Ominus, cls_not__less__eq_1, cls_Diff__subset__conv_0, cls_image__vimage__subset_0, cls_inj__on__image__set__diff_0, cls_less__supI1_0, cls_min__less__iff__disj_0, cls_minus__diff__eq_0, cls_Int__Un__distrib2_0, cls_compl__eq__compl__iff_0, cls_inf1E_1, cls_class__ringb_Onoteq__reduce_0, cls_Diff__triv_0, cls_minus__minus_0, cls_insert__iff_1, cls_le__maxI2_0, cls_insert__subset_0, cls_comm__monoid__add_Omult__assoc_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_sup__inf__distrib2_0, cls_inj__on__Un__image__eq__iff_0, cls_add__left__cancel_0, cls_less__minus__iff_0, cls_derivs__insertD_1, cls_fold__graph_H_Ointros_I2_J_0, cls_setsum__diff1__nat_1, cls_min__max_Oinf__sup__distrib2_0, cls_class__ring_Osub__add_0, cls_card__insert__if_0, cls_lower__semilattice_Ole__infI_0, cls_ab__semigroup__mult_Omult__commute_0, cls_card__Diff1__less_0, cls_inf__sup__distrib1_0, cls_vimage__UNIV_0, cls_order__less__trans_0, cls_neg__less__iff__less_1, cls_Int__absorb1_0, cls_conseq12_1, cls_add__cancel__21_1, clsarity_fun__Lattices_Oupper__semilattice, cls_fold__graph_H_Ointros_I1_J_0, cls_inj__image__subset__iff_0, cls_fold__inf__insert_0, cls_lower__semilattice_Oless__infI2_0, cls_le__sup__iff_0, cls_ComplD_0, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_inf__left__commute_0, cls_disjoint__eq__subset__Compl_0, cls_lower__semilattice_Ole__infI1_0, cls_inf__commute_0, cls_inj__image__mem__iff_0, cls_inj__image__Compl__subset_0, cls_mult__less__cancel__right__disj_3, cls_finite__insert_1, cls_diff__eq_0, cls_Compl__partition_0, cls_COMBB__def_0, cls_class__ringb_Oadd__mul__solve_1, cls_vimage__Compl_0, cls_subset__insert__iff_2, cls_Min__Un_0, cls_sup__compl__top_0, cls_fold1__Un2_0, cls_fold1__strict__below__iff_2, clsarity_fun__Orderings_Otop, cls_less__max__iff__disj_2, 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% 25.38/10.05  % No. of inferences in proof: 2085
% 25.38/10.05  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 9552 ms resp. 9020 ms w/o parsing
% 27.76/10.98  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 27.76/11.01  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------